Your SL1200 Mk 2 manual says the proper overhang is achieved with a 52mm distance between the stylus tip and the headshell plug. See figure 5-2 on page 1 of the manual (at least, that's where it's at in the manual available at Vinyl Engine). I would be surprised if any special tools would be needed to get good sound since I got good performance from a Stanton 500 V.3 in a Stanton STR8-80 turntable, whose underhung arm has much more tracking angle error across the record than your SL1200 should provide even if alignment is not quite spot-on.
If I recall correctly, you got a 500 body pre-mounted on a head shell and with the N500 stylus. I liked mine tracking at 3.25 grams. I don't really think it should matter, but if you've got the 2 gram weight screwed into the head shell, you might try removing that to see how it sounds without the extra mass.
Personally, I use a MFSL Geo-Disc. It's designed to provide Baerwald alignment, but I've liked the results even when used on turntables that were not designed with that alignment scheme in mind (such as a Well Tempered Record Player and a Rega RP3).