Sounds like a cool deck!
In reference to "sticky shed" -- tapes are the only things that can have sticky shed. This happens when the oxide of the tape (the brown stuff that touches the heads) flakes off and gums up, leaving behind a nice brown coating on your heads and tape guides. As long as you clean up the mess after playing a shedding tape, you should be in the clear as long as you replace the tape with a better/newer one that doesn't shed.
Is this machine a 2-head, or a 3-head deck? (erase, record, repro, or just erase and record head?)
If it's a 3-head deck just double check that the record head is completely clean. Also, check the wear on the head. If you see a noticeable "gap" down one, or both tracks, the head is shot. Look here for reference photos:
http://www.analogrules.com/badheads.html
Since this does appear to be a tube-type machine, it may be wise to replace all of the tubes. This will give your working components better performance, and may actually fix the record problem if, indeed, a bad tube was the issue.
Tubes can be hard to find, and pricey, so you may want to replace only the shot tubes. I'm not pretending to be an expert on tube electronics, but I believe that if a tube glows blue instead of yellowish-orange, it's either shot, or going bad. SO turn the thing on, let the tubes warm up, and watch the glow colors to track down suspicious tubes.
As far as relay are concerned, if your deck has them, check them out. If you're not familiar with relays, they basically are enclosed mechanical switches that switch signal or voltages. They generally make an audible "click" when they're switching. Sometimes relays get stuck, and just don't switch, either because the switching voltage is too low, or because the internal workings are oxidized, and are stuck. So that could also be a problem.
If you have a soldering iron handy, you may want to reheat some soldering joints, as cold soldered joints can be a problem. Just get the soldering iron fully heated up, and touch it to a solder joint for about half a second or so, just long enough to melt the solder, and re-seal the joint when you lift the iron off of it.
Another thing to look for, internally, is dry capacitors. Electrolytic capacitors are usually the culprits, and if you see one that looks like it's bulging out on the top side, that's an instant red flag -- get the specs of that cap and replace it asap. (NOTE: only electrolytic caps do this. Ceramic disk caps are generally fine for hundreds of years at a time.)
Hope that helped. Good luck!
Don't count on it, though ...