starting a 5.1 or 7.1 surround

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The Infinity Kappas are keepers. Hang on to them. They are beautiful too!
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Of all the equipment you listed, the 2 channel Adcom power amp and speakers can definitely be used in a 5.1 or 7.1 config.

Since we don't know budget, lets start the cheapest way - get a 7.1 or 7.2 channel AVR with a full set of PRE-OUTS. You can use the AVR's internal amps for your center & surround speakers. Subwoofer(s) are already powered. Run a pair of RCA interconnects from the pre-out L/R main jacks on the AVR to the RCA inputs on the Adcom. Hook up your Infinity Kappas to the Adcom and the rest of the speakers to the AVR. Run the AVR's room correction program and all 6 or 8 (sub included) will be equalized for your listening room. This config will leave the AVR to only have to power the center & surrounds, a task that most AVR's are up to. The Adcom still does the heavy lifting for the L/R mains. I really don't see how the Adcom pre-amp can be used in a modern HT configuration. You will get a tuner in the AVR.

Finally, if you don't like the performance of the AVR's amps, you can add a 3 or 5 channel amp (depending if you want 5.1, 7.1 or even 7.2) to the unused PRE-OUTs and still use the Adcom. Thats why you should get an AVR with full set of PRE-OUTS right away so your prepared in case you want to pursue this final scenario. Good luck!

I'm in a similar situation, Old 2-channel stuff, integrating with new. I have a new receiver as the control center that will run surrounds, and an old Yamaha MX2 amp (similar to the Adcom, but the Adcom's probably better) powering Infinity Kappa 7's (earlier versions of your 7.1's). Works great!