A Gatorbox or the like might be an interesting solution to this if you could find one — but then again, what "solution" exactly is it that you want? Is it to get a Classic or the like on the internet, or to connect to an Intel Mac (that might or might not be possible with the Apple IP Gateway), or is it to allow a Classic or the like to network locally with something running X.3 or below? The devil's in the details.
For its part, as you have discovered, ASIP in no shape, form, or revision will serve as a proper Gateway from pure Appletalk/ localtalk to anything TCP/IP. It does "speak" both languages, but that's about it. ASIP's multihoming capability is therefore really not of much use, except perhaps in large Appletalk-only networks where two or more large segments need connections to a central server, either to improve performance or to overcome the inherent numerical limits of Appletalk networking. Nor will ASIP serve as an Appletalk Router (which is what you describe trying to make it do in the latter half of your post). ASIP can relate to machines running the two forms of Appletalk, but it cannot serve as a bridge in the strict sense between the other two machines. Merely installing the free Localtalk Bridge Control Panel on your beige G3 would get you farther than ASIP, as it would enable at least a bridge between localtalk and ethertalk segments on an Appletalk network. This should work tolerably well with all systems up to X.3.9, though I have found LT Bridge to be less than reliable myself.
My own typically Luddite solution to the networking conundrum is to run Apple Internet Router (much more robust than the LT Bridge that is a subset of it) and Apple IP Gateway on an energy-efficient LC475, which also does very well indeed as an Appleshare 4 Print Server. It all runs at the same time, on a basic installation of 7.1, and my little LC has never crashed once in 2 years of 24/7 use. I have not fully explored the use of the IP Gateway, truth be told, as I have as yet had no real need for it, but I have read somewhere online that someone or other used it successfully in bridging older machines running old system software to newer ones running X.4, in which, of course, pure Appletalk is no more. YMMV, as might mine if I ever got round to trying it out, but quite apart from all that, with either it or the Apple Internet Router, or both of them together on your Q700, you'd maybe get all you need.
PM me if further interested.