I have a touring bike that was originally all Deore DX, but few bits are left now. The Deore DX triple crankset has a BCD of 110mm, not 130mm, for the middle and big rings. This is now a relatively unusual size, but rings are still available - I obtained a new 36T middle chainring from the LBS in '06. Remember that the capacity of the RD typically doesn't allow much more range (from granny to big ring) than 22T, so if you make your big ring bigger, that may need enough chain as to prevent your granny ring from working with any but one or two of the largest rear sprockets ( I'm running 24/36/46 on my Deore DX crankset at the moment).
I would consider converting the bike to 8spd with 9spd gear - you would need a 9spd chain, a 9spd right shifter and a 9spd cassette with one of the sprockets removed. Be warned, however, that the Deore DX RD may have too much play in it, being old, for crisp shifting with 9spd gear. This is what I found, even after replacing the "wide" jockey wheels with narrow 9spd ones, so ultimately I replaced the RD.
If you want to stick with 7spd, remember that an 8spd chain is effectively the same as a 7spd chain. (Not so for cassettes, of course).
Any 5 bolt, 110mm BCD ring of at least 46T will replace your big ring, but I would think twice about replacing it, unless you want to lock out your granny ring with the lower limit screw so that it can't be used. You don't need to use Shimano SG rings - as far as I know, these have long disappeared from production. 9spd rings will work, possibly better than SG. I have never worn out a big ring (my original one is still going strong) - are you sure that yours is dead?
I know that both 12-28T and 13-30T were the two standard cassettes fitted to the Deore DX rig - whether it is capable of running others, I can't tell you. I'm pretty sure that it wouldn't cope with 34T, but you may be able to use 11T at the other end.
