WOW! That bike is sooooo similar to mine. Are you sure it's not an '87? I bought my Diamondback Apex in '87 and it also has a U-brake. But I thought the U-brake was used on MTBs for only one year. Okay, maybe some '88s used them too.

Your rear hub is probably 130mm 6-speed Uniglide cassette. At least that's what was on most MTBs of that time. A very limited selection of Uniglide cassette cogs is available at www.loosescrews.com You can get complete cassettes as well as loose cogs. My bike originally came with 14-32 but I changed that to 13-28 almost right away. When I put slicks on it, I change to 12-26 for more road-worthy gearing (I bought a 12-34 cassette and loose 13 cog from Loose Screws and changed the 12-15-17-21-26-34 to 12-13-15-17-21-26).

If all you're looking for is a higher gearing, you could get a smaller cassette. You could also look into getting a larger chaining. A 50T or 52T would probably run fine with that crankset and front derailer.

700x23 won't offer much less rolling resistance than a 26x1.4" slick (or whatever you've got on there now). So I'd stick with 26" wheels.