Alex, I fitted 13 x 7.5J rims with the standard 19mm offset to the rear of my HPC and had to mod as follows. Grind a little off the corners of the De-Dion tube end plate, Turn the trailing arm mounting bolts around so that the roll bar links fit on the inside, and fit dished trailing arms from the superlight. The rear tyres are 8 x 22 ACB 10. I think you should be OK with 7J rims, but to be safe I would reccomend an offset of 10mm.
Re suspension I think your biggest problem is the front anti roll bar, which is probably too stiff. You don't mention which roll bar you have on the rear, but try stiffening it up a few notches before you do anything else. Trailing arms on track setting is also much better. I have 350Lb front springs, adjustable front anti roll bar, 200Lb rear springs, and 3/8" rear roll bar on one from hardest setting. This seems to work very well, but I was interested in some of the other comments about ride heights, does anybody have any figures for settings?