The crossmember is different for the square mounts vs the round mounts. You need mounts that match the crossmember.
So you need to either get the conversion mounts from driftmotion, or fab up your own, or else you need to swap the crossmember from a 1989.5-1992 A70 chassis. I would suggest that you get the mounts that will hold the square mounts onto a JZ block. Less potential trouble than changing the crossmember, with less in shipping charges.
@Turbo Habanero: The plugs on my harness were grey, but the yellow ones from a 1987 plugged right in. I suppose that if someone who didn't know were to look at the electronics in my car, they'd assume that my 1989 had a yellow plug harness, since it fits like factory. It's only if they started to compare to other cars and wonder why this one has a voltage gauge instead of a boost gauge that they might start to figure it out.
'89 was indeed something of a weird year for the Supra. Seems like Toyota didn't want to change everything all at once.