Tube Preamps?

A couple of things to consider. Most importantly what is the input impedance of your amp? If it is 10K which is typical in a lot of solid state you have to be careful as most pre-amps, especially the simpler less expensive variety, and a lot of the pricey stuff as well, have output impedances of 3500 ohms which does not predict a good match with a 10K ohm amp. If the amp is 50K or 100K it is usually not an issue. For example my pre-amp has an out put impedance of 600 ohms and ARC recommends amps with impedances of 20K. Could be you would not hear the difference. Could be. But at 3500 ohms you would.

You present equipment suggests to me that you are looking for a modest priced used pre-amp with a phono section. A good one (and there are many others), if the impedance issue doesn't exist, would be a Primaluna Three w/added MM phono stage. Its tone is easily influenced with changes in the tubes, it is rugged and dependable, on the warm side of neutral. It is very quiet as well. But it does have an output impedance of 3500 ohms so be warned. They are often available for about 1K and are easy to resell. If the idea appeals but you can only find one without the phono stage you can obtain and install one of these from a dealer. FWIW, it is especially nice when matched with the Primaluna 5 amp with KT88 tubes.

Hope that helps a bit.

The amp I have is an old B&K ST140. Sterophile (favorably) reviewed the amp way back when, and put it on the bench before listening. They rated the input impedance at 24.3k ohms. Since I am not much of an EE, I'm not sure if that's good/bad/something to watch.

My only idea is this: At one time I had a NAD 304 as my preamp, and I went with a Quicksilver Linestage using 12AU7 tubes (it was a very early model, SN 0005). That single change was as big a step up as I've taken since I've been doing this hobby.
Not a recommendation for a Quicksilver, but a recommendation to follow through on your hunch.