To repeat what was suggested in post #4 and post #9:
The way I do this here in the late 2010s is to have a 1980s unit stripe one of the tracks with a “FSK” sync tone. This is a special tone which sounds like a fax machine placed on one of the tracks with sync information (usually, by alternating between two frequencies) that can be converted in to a tempo sent over MIDI.
As far as I know, they no longer make dedicated tape sync units, but it’s easy to find old 1980s drum machines and sequencers with tape sync support; I recently got a Yamaha QX5 to do this for $50 which works quite nicely. Some late 1980s Roland drums machines (TR-626, R8, etc.) can do the same trick, also available for a good price on eBay. Be careful using an older Roland Drum machine with tape sync like the TR-909 (Paying $4000 to have something that does just MIDI-to-tape sync is one step removed from just burning money), TR-707, or TR-727; there are issues with those units running MIDI sync while being a tape sync slave (I believe there’s a firmware upgrade to the TR-909 which fixes this issue, but before spending $4,000 to solve your tape sync problem, please do some basic research)
To write the signal, what I do is, when starting a song, decide what tempo I want the song to have, then “stripe” (record) a sync signal at that tempo. Then, when playing back, I use one of the two FX sends to send that signal back to the unit, which then converts it in to a MIDI clock all of my other hardware can use.
For my last album (released in 2016), I did this with a Roland R8 drum machine, which did nothing on the entire album but read and write a FSK sync signal. For the current album, I am using a Yamaha QX5.
A couple of usage notes: The signal the QX5 uses is not compatible with the signal the R8 uses.
Also, there are issues with some newer gear dealing with the fact that MIDI starts but the BPM is 0 until the sync signal starts; my old ER-1 has little issue, but, as I recall, I have to start it before the sync signal begins the song. The Boutique sequencers need to be started within second or two before the sync starts otherwise they give up and go back to internal sync. The Akai Rhythm Wolf and Timbre Wolfs need to be power cycled before starting to lay down a new track every time, because they have a bug which makes them think MIDI start means MIDI continue.
That said, I have recorded an entire album this decade using this simple sync technique.