You are making it very hard for yourself by attempting to align your project to the original audio. Forget that. What you have to do is start by creating a midi session that follows the song correctly and starts at the initial tempo of the original tune.
Someone is going to have to figure out the tune completely, chords and all time sig changes if they are there. There is no getting around it. The best way is to still transcribe the original audio onto a chart. That
is the time to work with the original audio BTW. While you are figuring it out. DAW's make it easy to stop start and do sections at a time slowly. Don't worry about aligning the click to the audio.
Now you turn off the audio and construct a basic midi session that matches the songs arrangement perfectly.
Figure out the start tempo
Construct a click track (1/4 notes) and create all the time sig changes that match the song. You have just transcribed the whole arrangement onto a chart. You use that to quickly program up your session.
The idea is to create a basic arrangement/session in midi. What I do is put in a basic piano part that simply plays out the chord progression and a very simple bass line. I start with three things. A click that agrees with the music arrangement, a basic piano chord and bass track. Have at least two bars preceding.
For session musicians you can turn all the above into audio and give that to them along with the tempo info. They can align their DAW to the same tempo if they want but they don't even have to do that.
Next work with a guitarist/session players who can play out the entire arrangement and correctly. You need the chart at this point to give to the guitarist. You tell them there is two bars leading in. If they are good enough they will sight read the chart and play the arrangement perfectly. Even if they need to get it right in sections they can, but they must
only submit a total wave the whole length of the music back to you.
You should be able to align the start of the session recording in your arrangement and it should match your audio track right to the end. At worst you may have to cut in a few areas here and there and realign manually.
The original music may have some (more obvious) tempo variations on purpose as well as the time sig changes. You will need to identify those areas if you think they are important enough and if you feel they are, then you will have to program your original midi track to do something similar. And do all that before creating the first audio track for session players to play against. Otherwise leave it at a constant tempo. Live session players tend to play nicely around it anyway giving the track some timing feel.
Towards the end of your tracking work you drop out the original guide midi bass and piano. By then those parts may be replaced by live players or you sequence much better parts there. Drums may be a VST or a live player in the final mix as well.
This is how I have always done it for either original music or covers. Sometimes all the parts end up live, other times part midi and part live etc..I usually turn any midi into audio just prior to mixing.