Changes to older system

I’d replace the speakers first rather than trying to put a bandaid on them with tubes, and you probably don’t wanna run your Matrix 3s with a tube amp as they generally require some power to get the best out of them. Those older metal tweets are likely the biggest source of the brightness you’re hearing so fix the source of the problem rather than jumping through expensive hoops to get them to sound better. Given what you’re looking for I think you should give the LSA-20 Signatures a good look — they are available here direct from the manufacturer for only $1699/pr. They’ll definitely add more bass to your system, and their silk dome tweets will very likely tame your brightness issue without sacrificing detail. Read the reviews.

After that I’d upgrade the preamp as it’s the heart of your system and greatly affects the sound of your overall system or, even likely better and more cost effective, get good integrated that’ll upgrade your amp at the same time. Then I’d do a good DAC, and then I’d wrestle with cables. That’s what I’d do FWIW.

First and most obvious choice is cabling, but what?

Actually, wires are the last thing I’d worry about here, but a lot has changed/improved over the past 30 years so I think a complete overhaul is in order. Start by identifying which speakers really grab you and then I’d recommend finding an integrated amp that has enough power to drive the speakers and is a good sonic match for them. For a source I’d recommend an Innuos Zen Mk 3 that you can load all your CDs into and have all your music at your fingertips, and it’s also an excellent streamer so you can explore worlds of new music — much of it in high res. Only then would I address the cables. Anyway, that would be my plan of attack FWIW, and best of luck