No, you can't put an 8 or bigger cassette on your 7 speed hub; 8-10 speed freehubs are wider to accomodate a wider cassette. You can put a 7 speed cassette on an 8-10 hub with a 4.5mm spacer on the inside but not the other way around. If you changed the wheelset to one with a newer 130mm hub it would take a bigger cassette but I don't know if your 7 speed derailleur would be able to shift all the way up to the biggest cog, it was only designed to move far enough to span a narrower cassette.
You can buy 7 speed cassettes still, for example at
Harris Cyclery or
Loose Screws (I have bought from Harris and their service is great, haven't bought from Loose Screws but I have heard that they are good as well). If you upgrade the wheels and want to keep the 7 speed derailleurs you can get a spacer from either of them as well.
Do the chain and cassette really need to be replaced? Way back at the beginning of this thread you described the components as "near mint"; it is possible that those parts still have some life in them if the bike wasn't ridden too much.