Replace vintage NAD 7020?

I’m wondering about the best inexpensive way to upgrade my barebones and mostly vintage system. All advice greatly appreciated, as I am a real novice! I bought this budget audiophile system back in the early 80s: NAD 7020 receiver (same amp as the 3020), Dual 505-2 TT and Snell Es. A vinyl fan, I held out on getting a decent CD player until 5 yrs ago, when I purchased a Consonance Linear 120. At the moment I live in a city apartment, so most of my listening is through Sennheiser HD_250 Linear II headphones. I listen almost exclusively to classical music, esp string quartets.

I’ve been satisfied with this system, given my budget, and it has held up well over the years. But my impression is that audio QPR has improved a lot and wonder if I can start to move toward something nicer. My main concern is that the sound seems too “laid back”, and lacking transparency and detail. While I prefer this to something with an overly bright midrange or treble (I bought the Consonance player because of its slightly warm and “analogue” sound), I wonder if it’s time to replace the NAD. I can only afford ~$600-800 to upgrade, though. Would a newer SS integrated amp like a used Arcam, say, make much of an impact? I read conflicting things about how important the amp is to the overall sound, and some people seem to think very highly of the NAD 3020 even now. So is it the right place to put the $$? If so, should I look for an amp with a phono stage or go with separates (e.g. a used Cambridge Audio integrated and 640P phono stage, presuming that matching amp to phono stage matters)? If not, is the alternative just to save the $$ and think about new speakers when I have a place I’ll be able to listen to them again (which should be fairly soon). Many thanks in advance.