Hey Keef! (if that IS your real name...)
I've been using various versions of Sonar (now Cakewalk by Bandlab) to record for more than ten years at this point, almost always starting exactly how you're describing, basically treating the DAW like analogue tape. Recording full takes (occasionally disconnected sections) at a time of as many instruments simultaneously as I can and then editing them together after for a full take, which I then overdub on.
An example from my band's most recent album. "Acorn Armies".
https://summerjanuaries.bandcamp.com/track/acorn-armies We recorded four full takes of the song, playing drums, bass, guitar, and fiddle simultaneously. Then I assembled a master take after the fact from the two best takes, and then we overdubbed additional fiddle, vocals, banjo, guitars on to that master take.
The key to starting this kind of editing is to do the takes consecutively, as if it really were analogue tape. Just record a take, then whomever's running your session hits the spacebar to stop things, then hit CTRL-S to save. Then advance the session just a bit and then record your second take, after the first. No overlap, no problems with selecting all the files, no problems PERIOD. Just the takes all laid out in a row. Makes it easy to drop markers too to mark any of your thoughts and identify sections that are good etc. Once I've selected my "master" main take, I usually copy it over to the end of the session (past the whole takes) then chop out any bits I don't like and go fishing for replacements for those sections. If your tempos are consistent, and you edit along the entire take (every instrument) this can be a really smooth, even fun process. Usually totally painless for me.
Happy to help with any other questions you might have about this process! I find that people usually get distracted by all the bells and whistles and tend to forget a DAW can just be a tape recorder, you know? Just the most consistent, best maintained multitrack that ever existed!
If anyone's interested, here's a walkthrough video from the song linked to above, that shows where everything was situated during the take (literally walking from station to station while we tracked the first or second take of the song!)
https://www.youtube.com/watch?v=HrRYKR5yHnY