Is my 1988 Nakamichi OMS-1 worth repairing?

Absolutely not!!! Buy an Adcom GDA 600 DAC and use your dvd player as a transport. The Adcom is usually available for $175-225 on ebay or here on The Gon. It is a magic box which sonically beats the pants off any cd player you could get for under a $1000. I can not stress strongly enough how good this unit is. It is insanely good for the money. For a few dollars more you can get the GDA 700 which is basically a GDA 600 with HDCD.

I wouldn't repair it.
I repaired a OMS-7A (new laser) and regretted it, as the repair cost exceeded its value and something else could easily fail in a player of that age.
You should be able to find a far better sounding used player for little more than the repair cost.

IMO, there is no 1988 CD player worth repairing.

Dopogue is right. Older technology CD players are junk for transports. Get yourself a Sony or Philips DVD player with dual-laser, such as the DVP-S7700 or 9000es and get it modded. A superb transport once modded.