Well I had a Kenwood integrated with a Technics table, used the Kenwood for many years as a pre-amp with a Dynaco amp, before migrating gradually to way more high-end. Like you I was real happy with what I had, only it was very old, some of it starting to fail. When it comes to audio I've always been a value shopper.
I'm real happy with the way things turned out, in fact was happy pretty much every step of the way, so you might be interested in what and how I did that.
Well first and foremost I went and listened. Unless you are stranded in Pitcairn Island there's always a way to go and listen. You just have to make that a priority, which you will once you understand there is nothing more important that you could possibly do. Read, sure. Talk and ask, of course. But go and audition. Whatever it takes. I went everywhere, sometimes toting along my own CDP or interconnect, or even one time my own amp (!) to compare in the store system what I couldn't bring home to compare in mine.
Huge amount of effort. Totally worth it. Invaluable. The few times I let myself be convinced and bought something I thought would be great at what seemed like a steal, but without auditioning, it turned out to be a dud. The few times it wasn't immediately apparent it wasn't long before I found something by auditioning that was not only better but hugely better and at a better price as well.
Also what you will learn by listening a lot, you will come to find patterns. Like most manufacturers have a "house sound", there are similarities between amps built around the same tubes (6550 or KT88, etc) and a lot of these products have fairly long production runs. So if you hear say a new integrated tube amp in a store and they've been making it 10 years with few or no changes that counts as an audition and you can be pretty safe buying used. If you get to that point don't be shy about asking the store to let you audition the new one before you go and buy the used one! I did that and so knew for certain the McCormack DNA-1 was gonna make me happy. Then I found one used for a lot less.
Sweet as the McCormack was it is still a separate amp which needs a pre-amp, which means additional interconnect, power cord, cones, etc. By luck I was able to audition an Aronov LS-960I integrated which while only very slightly better sounding than the McCormack cost less even before counting what it saved me in interconnect, power cord, etc. So you are on the right track looking to simplify with an integrated. Smart move.
The Aronov started blowing fuses and they are unfortunately out of business (unbelievable deep wide imaging and with bass every bit as good as the best solid state, so a shame they are gone) and it was replaced with a very similar Melody I880
http://stereotimes.com/amp110807.shtml which would almost certainly fit your requirements- if you can find one used and figure out a way to hear one. If not there are plenty of affordable tube integrateds to choose from. Just whatever you do be sure to listen first.
