[Occasionally6]

There's no doubt a mid-engine conversion, properly done, would be very cool but it's not a trivial undertaking to do it. It's more than just moving the engine from the front to between the rear wheels. You will essentially be designing a whole car from scratch.

Mid-engine and front engine, especially with FWD, require very different suspensions, because of the different weight distributions and forces on the tires. FWD steering and suspension is affected by the wheels being driven rather than being dragged (pushed), with the suspension geometry set up to compensate. Both ends of the car's suspension system have to be redesigned.

Like niky and Frank Lee, I think it likely to make the thing handle worse rather than better by moving the driveline.

Because it's J-body there's got to be a heap of different anti-roll bars that will bolt on or can be made to do so. Even if it didn't come with one from the factory, different models that share fundamentally the same chassis did. There will also be some available from the aftermarket as upgrades.

You can get scientific about the size(s) to try but empirically maybe a good start would be to find out what was used in V6 versions of the J-body (18mm ^?) and try some of those. They're going to be really inexpensive to buy because they don't wear out.

Without checking the full back story on the car, it originally had a 2.2ohv in it and now has a 3800, correct? Did it get stiffer front springs, to compensate for the extra weight, at the same time as the engine swap? The springs will also contribute to the roll stiffness of the car and its handling balance. As a simplification, the end of the car (pair of wheels) with the greater roll stiffness will lose grip faster than the softer end (pair of wheels).

One thing that may be happening to cause snap oversteer with a soft front end is for the rear suspension to run out of travel in droop while there is still load on the inside rear wheel. That will result in the immediately transfer of all the rear cornering force onto the outside rear wheel and a net reduction of rear grip - oversteer.

As an aside when Nader vilified the Corvair, in part by levelling the accusation that the 'dangerous handling' was due to the engine location and resulting rearward weight distribution, GM conducted some testing with vehicles of various configurations. The conclusion was that, in a four wheeled vehicle, the handling can be balanced, largely by altering the differential in roll stiffness at each end of the car, regardless of the static weight distribution.