While I do lock my tape deck to my DAW via SMPTE/MTC...in reality, if your deck has a solid, stable transport/internal clocking mechanism...who cares about making it sync directly to the DAW!
Here's the way to look at it.
If you slap a click on one track of your deck and then record on the other seven tracks, those tracks and the click will all be in time...right?
Now...dump the seven tracks AND click track into the DAW.
Go back to the deck and erase the seven music tracks, but leave the click.
Now record seven more tracks and again, just dump them and the click (again) into the DAW...no need to worry about synchronizing to the existing seven DAW tracks...just dump as close as you can to the other tracks.
Once in they are all in the DAW, group-select either the first eight or the second eight and just drag/align them to the other eight tracks, using the click tracks as an easy visual guide.
Keep in mind that your song tempo is always the MAIN "sync" of any song...right?
So if you just play it the same way, using the same tempo (the click track guarantees that)...the song will always start and end the same, and will always be the same length and speed… your sync will be no worse than any 5-6 guys playing together in a band.
And even if your deck slowly changes it's speed a bit as the tape winds from one real to the other...it will do it relatively the same amount every time, since you are going to record each group from the same point on the tape.
Of course after 3 maybe 4 dumps (that's 21-28 music tracks), you want to stop...but if you use good tape, it will withstand those passes...and after 3-4 dumps, you've probably gotten as many tracks as you'll need for most Rock/Pop tunes.
Finally, if you do notice a bit of drift towards the end of the song between any of the groups...well, just use the click tracks and cut/adjust as needed.
Just make sure to keep each of your 8-track dumps grouped, so that way, if you have to cut/adjust, you will do it across all the tracks from any one group.
My deck has a very stable, microprocessor controlled transport…but I’m not sure how stable the TSR-8 is...?...but hey, give it a try. I mean, you are already having sync issues trying to lock to the DAW…so just take that out of the equation, and see how stable the deck is by itself. All you need to do is align the tracks after the dumps.
Am I way off base here…?