To be clear:
The fact that the band is by common agreement the owner of the recording rights to the original album master is totally irrelevant to who owns the musical composition rights of the individual songs on the recording. 
Unless there are some unspecified factors outside of what you have said so far, you own the musical composition rights to the melody line and lyrics that you wrote. You can do anything you want with that melody and lyric only. 
Unless there are unspecified factors not mentioned above, the presumption is that the actual author/inventor of the guitar part owns the musical composition rights to the guitar part. The fact that the guitarist has not registered his composition rights to the guitar part as a separate composition is totally irrelevant to his ownership of those rights. Unless you can show that some written agreement signed by the guitarist assigned (transferred/sold/conveyed) his composition rights in the guitar part to you, the presumption is that he still owns those rights. Under the presumption that the guitarist owns the musical composition rights to the guitar part he wrote, you use his composition at risk of infringing his musical composition rights in the guitar part if you copy it in any significant way when you do your own performance, unless you obtain his license to do so. If the guitarist as a person refuses to grant you a license, you can obtain a compulsory license, because he, like you, made his composition rights subject to compulsory licensing by permitting his work to be published as a recording. But you will have to pay the statutory fee for each copy made under a compulsory license. 
 
There are several ways that you could overcome the presumption that the guitarist owns the musical composition rights to his guitar part. And you may be able to mount a successful defense to a complaint of infringement, but bottom line, that is the presumption that you are going to have to refute in court. The way professionals in the entertainment business handle this kind of dangerous ambiguity is to get a license for what they want if it is cheaper than the risk of going to court, or by using original or different licensed material from another source instead of the iffy stuff. If it turns out that they could have used the material without a license, the cost of a not entirely necessary license is considered a wise investment nonetheless. An infringement lawsuit is going to expensive for everyone involved, and only one party is going to come out as a winner in the legal sense. Unless the monetary value of the new recording is going to be big, the outcome of a lawsuit will still leave everyone a financial loser. You can hope that your guitarist will be deterred by that  practical realization, or you can do what the professionals do and clear the rights you need. 

Or I can just save everyone the headache and decide not to include those songs on my new album!  But they're really neat songs, damn it! :)
 
Thanks for the clarification.  I understand what you're saying now.
 
So here's another question to further muddy the waters: are there any guidelines outlining the parameters for what would constitute a "cover" of those additional musical elements? To use bapu's earlier example, I'd think it would be pretty difficult to claim copyright infringement on one of Ringo's drum patterns (especially for their earlier) work since they're pretty common patterns used everywhere.  Similarly, the drum patterns on Songs 1 & 2 aren't terribly unique, so while a beat-per-beat copy of the entire performance would be a no-go, at what point does one cross the line between "similar style" and outright copying?  I'd heard once at some point that for a melodic line (such as a guitar solo) that "seven notes" was the limit - if anything more than seven consecutive notes lines up exactly with previously recorded/copyright material, it's infringement.  I have no idea where I heard that or if it's the least bit accurate.

The determination of what constitutes significant copying or of what is sufficiently original to qualify for its own copyright in a particular instance is undefined in statute. The only way to find out for sure is to copy it and see if someone sues, then let the judge or jury decide. Precedents include tests to guide their decisions, but the tests are not as simple as "how many measures." A judge or jury will be asked to decide if there is substantial similarity in the works, and if so if enough of what was valuable in the original was appropriated that it is actionable. In general the line is much clearer for sampling of a recording than it is for copying music. That makes sense, in that it is nearly impossible to argue that the exact sounds captured by a microphone could be independently created, or accidentally duplicated. Bridgeport Music v. Dimension Films held that a sample of any length of a recording was infringement. The ordinary listener will be more likely to determine that a recognizable musical motif is appropriated, original, and valuable than that a drum pattern or base line is. Chord progressions are generally so common that they get a pass. Independent creation is an absolute defense against infringement, but substantial similarity and access to the original will generally be interpreted as proof of copying. So if I could prove that I was raised in a cider keg and only received gruel through the bunghole. with no other contact with the world prior to writing my version of Red October, even if it were word for word identical to Tom Clancy's work, I should be acquitted. You clearly do not have that option with band material. 

Just a quick update: I have a consultation scheduled with an entertainment attorney next week, but I did spend a few minutes on the phone today discussing the issue at hand with the attorney, and she states that I'm clear to do whatever I want with the songs I wrote, just so long as I don't use any samples from the recordings of those songs.  She said that because I have sole authorship of Songs 1-4, I can re-record them in any way I see fit.  While authorship only covers lyrics and melody, unless separate copyrights had been registered for all other elements of the song (which they hadn't), my registration via the PA Form has me covered.
 
She also stated that, while not a legal matter like copyright registration, the fact that all of our songs are registered with ASCAP in accordance with how we set up the copyrights (copyright authors=ASCAP writers; sound recording copyright=ASCAP publisher) demonstrates consistency and further reinforces the fact that as a group we'd decided to grant song authorship to specific people based upon their contributions in the creative process.
 
That being said, I am going to reach out to the other band members and let them know that I'm re-purposing those songs for my new album.  If there are any hard feelings or issues with that, and/or if I think one or more of them may fight me on it, then I'll have a decision to make.  Legally it appears I have a strong case and I'm covered, but I'd need to decide whether a lawsuit is worth it, and may ultimately end up creating a different arrangement, whereby I'm not replicating any of the musical phrases/parts I didn't compose.
 
And who knows, maybe they'll all say, "Awesome, dude!  Good luck on the new album and can't wait to hear it!" :)
 
Thanks for the continued feedback and I'll follow up again next week after I meet with the attorney.

bapu

BobF
Don't forget that Fogerty got sued (and lost) in a case for plagiarizing his own work.

Urban myth as I see and remember it.
 
http://mentalfloss.com/article/27501/time-john-fogerty-was-sued-ripping-john-fogerty
 
In the original suit about the two songs, Fogerty won. Then he sought lawyers fees in a separate suit, which he lost. But, he went to The Supreme Court and then won the argument that he was due Lawyers fees.
 
He DID NOT lose the case involving the two songs which Zantz of Fantasy Records brought to trial.

I was lied to!!
 
Hey, it was still a huge hassle for him.