When my Healey was an active autocross contender, I ran a 3/4" rear bar in conjunction with a heavier 7/8" front bar, both sourced from Addco, IIRC. Under those conditions it was a big improvement over the stock configuration (and easily rotated with the throttle).
Tube shocks were still a no-no in the street prepared category, so the valves in the stock (new replacement) Armstrong shocks were shimmed and tightened up a bit, along with variety of Castrol motorcycle fork oil viscosities.
When I tore the car down for restoration in 1986, I did away with the rear swaybar AND the Panhard rod, and fitted an articulated A-arm to locate the axle instead. Try as I might, it is very difficult to induce either under or oversteer__I don't know if the tires are that much better, or if I just lost my nerve, but the car seems to be very well planted now, with neutral balance
Overall, my impressions through decades of modifications align with Michael's observations.