Seems like the SG Melody Makers are no longer available in the U.S., at least through any of the websites I've checked, and there are a couple of LP models, w/either one bridge HB, or two P-90's?
The Melody Maker model with one pickup in the bridge position is going to give you a limited range of tone, IMHO. A lot of the sound associated with SG's & LP's is the smoky, slightly dark sound of the neck humbucker, a sound you won't be able to get from a bridge pickup. It will be a slightly different sound from your Strat, but perhaps not as versatile, more suited for rhythm than lead. It probably won't quite make the cut as a Jazz guitar, but with a little tone-sculpting, it's a fun, lightweight guitar for just about anything else you want to play.