Will McIntosh C2600 tube preamp solve my problem?

The C2600 will likely warm things up a little. Does the dealer offer a return policy? Is this the same dealer where you purchased the B&W’s? and the Rotel? One of the higher powered McIntosh integrated amps would be a great idea, however I cannot recommend an all tube integrated amp. The measurements and comments in Stereophile’s review of the 803 D3 suggest it is a demanding load and not suited for a tube power amp.

All good questions.  Yes, I'm open to used.  And yes, good suggestion to "demo" the C2600--I'll ask.  You ask about dac, yet sorry, not exactly sure what that is (I was serious about being limited in knowledge--much has changed in 35 years). No need for phono stage.  Don't know what "true balanced outputs" are......  Listening levels are low to medium and I listen to 70s classic rock, jazz, some contemporary musicians with strong vocals like Adele, Bareilles, Norah Jones, Krall--a wide variety of interest, but nothing heavy and loud. 

In your situation, it seems that a good approach may be, the simpler, the better, since it is going to take a while to get back "up to speed" on everything. Using a tube amp definitely doesn’t fall into the simpler category, as there are more speaker compatibility concerns to be addressed, and also because the tubes themselves at some point will need attention.

For you, I like the idea of an easy to use solid state integrated amp. McIntosh makes some really nice ones, and the new Anthem STR integrated looks nice as well. Both should have what it takes to drive the 803s decently.  With regard to your interest in "warming up" your sound, you should know that the McIntosh MA 8900 integrated amp includes extensive tone controls, so that you can tailor the sound to your liking.

I’m surprised that a dealer suggested a tube amp for those speakers. Also, I strongly recommend getting out to as many dealers as you can to see what’s out there now days, and, at this level of equipment, I’d suggest working with a dealer for future purchases. It’s real easy to purchase equipment that does not complement very well the equipment you already have, such as the 803s.

Please note that the C2600 is not an "amp", it's a tube "preamp".  Also, several respondents are referring to 802 D3 and I have 802 D3 speakers. It may not make a difference, but I wanted to point out exactly what I have since there's some confusion.  Thanks for everyone's help thus far.

"Also, several respondents are referring to 802 D3 and I have 802 D3 speakers."

Sorry, my post was a typo. The Stereophile review was for the 802 D3. 

What are you using for the source component?