... should I Buy a New Integrated, or upgrade/update/rewire my existing...

No doubt that wise modification choices can improve the sound quality of your Onkyo amplifier but only to a certain point. As has been mentioned the speaker plays a major role. I would ask what is your ultimate objective? If you’re willing to spend up to 10 K dollars for an integrated  amplifier you have a multitude of wonderful choices available to you. What type of music do you listen to most often? With proper planning and execution you can create a superb system. The key is to define what you really want. There's a lot of excellent sounding components available out there. 
Charles,

From a post on 5/14 the OP currently has JBL L25 speakers and is waiting delivery on Gershman Avant Garde RX-20s speakers.

Yes, a slow morning.

... nice detective work acman3: you are correct, except I didn't include the pair of University S6 labelled "The Master" from the 50s (presently not playing)...

I am turning 63 this week and want to just simplify - have made myself (and others) crazy for years with electronics, and finally come to the conclusion that it is the music that's important to me, not so much the glitz and pride of ownership in audio jewelry...

I have been a vintage guy forever (maybe what you cats call mid-fi): from Sansui, Nikko and B&O receivers, Marantz and Linn CDs, thru esoteric tube (Wolze) and SS (Accuphase, Phillips and McIntosh) pre-amps; PS Audio, Accuphase, McIntosh, Linn, Nikko and Onkyo Integrated and/or Power amps, and JVC, Sansui, Acoustat, Sonab, Mark & Daniels, Criterion, University, JBL (now playing) and on-the-way refurbished Gershman Avant Garde RX-20s speakers... ALWAYS JUST VINTAGE STUFF.

The only pieces I anticipitate keeping are the JVC QL-A7 TT I'm about to replinth and recondition, a Sanyo PLUS T35 Tuner, the Phillips High Fidelity Labratories Pre-Amplifier ( just in case...) and the Gershmans; new? - will probably go with ModWright/Oppo CD and then the dilemma of a pre/power pair from one manufacturer, or an integrated amp. I just figured that an integrated would be the easier way to go (as long as its got pre-outs and main-ins for flexibility, in case I can't rid myself of the bug, which is why I'd keep the Phillips) -  and why not get something TOTL, like a GamuT or a Rowland, to keep for the rest of my life.

Times change - and so am I - trying at least...

Music runs the whole gamut except Hip-Hop... Test tunes include selections from Cantata Domino (Oscar's Motet Chior), Pink, Kansas, Walt Disney, Dead Can Dance, Bieber, Queen, Coltrane, Miles Davis, Eagles, Holst's Planets, Rebecca Pigeon, Stevie Wonder, Jennifer Warnes Famous Blue Raincoat, Red Hot Chili Peppers, Styx, Willie Nelson, The Sounds of Space (5 CDs), Elton John, Dixie Chicks - I can go on but I guess you get the idea...

SO yeah: I guess it is probably a LOL conundrum I'm imposing on myself - maybe I should just go with a One-Box AVM CS2.2 Everything Included and wing it from there...

I've had some vintage gear upgraded and the results were very nice, but the Gershmans deserve way better than an upgraded A7. But, keep and enjoy the Onkyo also...