Adding a bigger bar to the front is the wrong way to go imo(unless your running a stock class vw perhaps),the end that loses grip 1st is the end to soften not make stiffer as its already transfering too much weight.
Soften the front 1st(assumming your alignments in the right place),get as much grip as you can find and once your there than tune the rear with stiffer springs,bar and shock settings for the balance you want.
Always tune the end with the least grip 1st,makes no sense to try and reduce the rear grip to balance out the front without 1st optimising the front.Also if your looking at a different tire I wouldn't spend too much effort tuning with the stuff you have now,sticky tires will need a different alignment and roll stiffness front and rear to get the most out of them.