What springs? What are doing with the rear suspension?
Sway bars are typically the last tweak, with rate chosen to fine tune roll couple. To just say "a 7/8's bar is right" or "1 inch is best", you need to put it into context with the rest of suspension items that effect weight transfer rate. I don't know if both tubular and solid bars are currently available, but that's another consideration, as (duh) they will have very different rates for a given diameter.
I'll be curious to hear what people who have tested different bars and combinations of bars have to say, like Buck. Most Tigers I've driven push too much corner in/mid corner. Normally, I don't think it is a matter of too much front bar stiffness (there are other more common causes), however.
I'm currently running a 7/8" front bar with 350# springs. Out back, no bar and a home made spring bundle of stock Tiger with one extra primary leaf taken from an Alpine...maybe 180-190#? I'd like more front bar to lessen roll up front, planting the inside rear tire better mid corner/corner off, but am unwilling to put up with what the change in roll couple would mean to front end grip. I will say, in comparison to a number of other Tigers I've driven, my car works very well. But, I'm certain there is a bunch left in it, for sure.