I'm not aware of any successful DIY reel grinding rigs. The process demands a level of precision not normally achieved with ad-hoc methods.
If you are 100% on wanting to do it yourself, best bet is to buy a used grinding setup and learn to use it. (Buying/renting a trailer is cheaper!) If you just want to face the bedknife, there are handheld tools for that, as simple as a regular mill file or for something a little faster, a converted angle grinder.
You can backlap the reel regularly to help maintain the cutting edges. That's something you can certainly DIY, as you only need to figure out how to adapt a motor to turn the reel in reverse. It can be as simple as using a cordless drill, socket adapter, socket, and the appropriate size bolt, or you can build/buy a dedicated machine to spin the reel. The latter is usually cost prohibitive to maintain just one mower.
It's not uncommon for some smaller golf courses to maintain their reels via a travelling service. If you ask around, I bet you could get a name or two, and maybe have your machine done when they are in the area.