Sorry for the delay updating.

I got the reels repacked, which was pretty easy. That got a lot of my drift taken care of, but I still have some. If I tilt up the heaviest pallet we have (~2500 lbs) it'll still drift down in a couple minutes.

To figure out where it's leaking, I tilted up a heavy pallet, then disconnected the hydraulic line that's pressurized for tilt-down (rod side of cylinder) right at the reel connection. While it drifted down, I saw no fluid exit this line but a couple of drips. So I'm thinking this tells me that there is no leaks in the reel or cylinder (again, no external leaks), which I'm thinking leaves me with the tilt valve itself.

Thinking that there might be some o-rings in there, I very carefully took the valve apart. I'm sure you already know it doesn't. Everything looked fine: I couldn't really see any real scores on the spools or the bores, however there were some marks. Defeated, I cleaned it carefully and reassembled it.

But I think it has to be the valve since the fluid has to be going somewhere, and it's not coming back down the unpressurized line. One thing I haven't done yet is to change the hydraulic fluid. Wishful thinking, but perhaps it's gotten thin? The plate calls for SAE #10, I've been using HF32. I assume that's correct for indoor use?

Wow, thanks very much for the help! Yes, the reels are like mrfixit says; the mechanical part of the hydraulic joint is way out separate from the sprung part, so you don't need to mess with recoil part of the unit to work on them. It just floats and the hoses keep it from rotating.
I can't detect any play in them so I don't think they're worn, just that the seals are old (extension side has a minor weep I might do at the same time). Even if the repair didn't last long normally, I think it's worth doing since the forklift sees little use. Records show something like 10-15hrs / month.
Up to now I've gotten pretty good service from the local dealer. This experience has been a bit disappointing, but I suspect their hands may be tied in this case.
I'll let you know how it turns out. Thanks again!

The tilt on those old machines consisted of the tilt cylinder, hose reel, and the control valve with a lever on it, no solenoids. If that is an original reel the swivel pulls right off and the sealing rings are right in there. Remove the snap ring or bolt that holds it on and take it off. There is no need to remove or disassemble the reel. There are 3 square shaped "O" rings in that outer swivel piece, Raymond # 530-665, and they are available. Make sure you are working on the reel for tilt, the forks are tilted down, and you have a drip pan ready to catch some oil. Should be 15 minutes labor and $20 for the special "quad" rings. $2100 !! What is this world coming to.

I'm in agreement
It's been a while since i worked on a model 20. Tilt is controlled by tilt cylinders, via a solenoid and a valve, which is coontrolled by a lever.
Hose reels can be repacked, but the older Raymod ones do wear out and honestly the packing kits for them are a pain, and often fail again quickly. Also, they are spring loaded and I have seen several techs badly injured by the spring. It may be the dealer does not repack reels because of that.

well replacing the hosereel does seem a bit extreme unless its worn out and leaking or something
if they checked the tilt cylinder and it wasnt leaking by internally then i'd go looking at the control valve or any solenoid valves that may be controlling it.
generally cylinders drifting are caused by internal packing being bad, leaking seals or a bad control valve or solenoid controlled valve.