Hi,
Actually you will probably be able to find someone who does 100% analog if you look for it.
Ask the guys who do the mastering/writing on the lathe - they're the guys who really do your vinyl mastering and if the guy knows what he's talking about he'll be able to use a stereo 1/4 inch machine that goes straight onto your vinyl from your own master tape (the guy I work with unfortunately for you is in Paris but he knows how to do it and has since the 60's).
I recorded last week-end with a Tascam TSR-8 which is a more modern machine than yours but it works great just the same. I'll mix down going through a standard mixing deck using auxed out spring-reverbs, boosts and tube preamps in the inserts and master straight into to a revox A77.
Make sure you boost your input signal on the TEAC and use those nefty saturations that the stereo deck plays you - that's where you're mastering.
Regarding the speed, for a stereo you're on a standard with 7 1/2 so no worries. The idea is that the speed increases the quality because you're writing on a wider area of tape. So a 1/4 stereo @ 7 1/2 IPS is the same quality as an 8 track 1/2 inch @ 15 IPS (add it up, you'll see it works...).
Any mastering studio today (unless you're in with the rare guys who still do it) will use digital. So you want to master yourself really. Your mastering is actually on the stereo 1/4 inch and the pre-amps take all the peak signals in (doesn't work on digital and you have to cut stuff out to get it to sound right). Hence the advantage of mastering yourself on that sweet stereo deck of yours.
Once you're on a 1/4 inch tape, then you can stick it into a soundcard if you want the digital version and - wohay - it's already mastered.