Should I eliminate my preamp?

Since you already have the components, listen with your own ears. For me, I prefer having my Oppo 105D going into a processor or preamp and then into the amp. That sounds better to my ears but possibly not for yours.

(((This is a very smart move)))
 I strongly disagree......
((( Adding an extra link in the chain can only degenerate the signal. ))))
If your listening to a preamp with 55 cents integrated circuits you may be right
At first, it may seem cleaner with elevator music yet try it on something with
dynamics. As Mcgal suggested try it yourself and listen.
 You may have also discovered you need new tubes or different brand type installed.
 What is model pre amp it?
 Best JohnnyR

My preamp is AR SP6 b (circa 1980).

I thought using the volume control on a digital device such as the OPs UDP would degrade sound from truncating bits at lower volume settings, hence the need for a pre-amp with (presumably) quality volume control in the analog domain.

The argument about dynamics is wrong. An electrical signal comes out of the Oppo and goes into the power amp. What would be pre amp do? Change the signal?
As for digital volume control. That argument was true years ago. These days DACs have enough bit depth to avoid this problem. There is a paper by ESS somewhere but I do not have the time now to look for it.