I disagree that the LS1 would significantly throw off the balance of car. If anything, the LS1 conversion might even handle better than an E30 with an M20 - the M20 weighs 440 lbs, and if the LS6 really weighs as much as you say it does, then an LS6 would probably be comparable to a six pot E30. It's doubtful that he has an LS6, though. If he did, would have made a big point out of it and wouldn't have even mentioned the LS1.
Irregardless, I wouldn't buy it for $15,000. If I wanted an E30 with an LS1, I'd buy a junkyard LS-1 and T-56 for about $3000 or so (the current going price) and throw it in my E30. Adding $1000 for miscellaneous stuff that would be needed to complete the conversion, I'd have a total vehicle investment of about $5500 if you include the original purchase price of my car. $15,000 is steep.