It does accept MIDI Time Code, but doesn't that require that I be sync'd to a DAW? (Which I am not)
There are hardware boxes that convert between SMPTE and MIDI time code. The synchronization principles are the same, but the time code is actually different. MIDI time code isn't tied to standard video frame rates, so you don't have the drop-frame tricks to deal with, and you actually have better time code resolution with MIDI than with SEMPTE time code - except that if you're starting with SMPTE, the resolution can never be better than that.
A nice vintage JL Cooper PPS-100 will solve all of your problems. There are a a couple for sale here on Reverb dot com
And you can read the manual here
I thought the straightforware MTC-SMPTE conver things were common enough so that eBay would be loaded with them for about $20 or so, but I didn't find anything of interest there, which suggests that I should continue to hang on to my Music Quest Framelock just in case.
But, really, you should just temporarily turn a computer into a time code generator with that on-line time code WAV file creator you found, play it into your tape deck, play your tape back into your console, and play around with the levels until you get reliable time code lock.