Interesting challenge. Once you add Blue-ray, you'll pretty much be required to update the TV, though. Blue-ray uses HDCP, which is a form of copy protection that tries to confirm that it's playing to a real TV (looks right through the AVR). The player sends out a request for the display to ID itself, and if it does, the player will play. Your TV simply has no way to answer, even if the AVR did scale 1080p down to it's favorite flavor. So many Blue-ray discs simply won't play. No point to that. No magic converter box would be worth the trouble either. Be prepared for analog sources like the Laserdisc and VCR to start showing their age once the TV is upgraded. Those sources don't upscale as well as the DVD, and will tend to look pretty nasty by comparison. Not much you can do, just be ready for it. Most of what's wrong with those sources is now hidden by your vintage TV.
You might also want to consider moving as much as possible to HDMI now to conserver precious analog inputs.
Also, if you're doing Airplay, you'll probably eventually want to load all the CDs in the multli-disc player into a server for easy access. Again, Apple TV will work for playing all that to the system, and the process gets you better control, visual album art, playlists, etc. All things the player won't do. Save another analog input in so doing.