It is not really a "performance car"... more a warm hatch. It is quite badly compromised from a performance perspective by being front wheel drive. That in combination with significant torque will mean that wheelspin is likely at wide throttle openings at low speed.
Now the tramping issue. I'd never had tramping (the original fronts were Contis, replaced by PS3s). Today, in the interests of science

, I left a gap in a queue on the M6 and nailed it from a standing start... The much vaunted PS3s tramped

. Admittedly, I was fairly brutal... so is it a tyre issue? Partly. Is it a suspension design/construction issue? Partly. Is it a road surface issue? Partly. Is it a temperature issue? Partly.
I feel that with the Bridgestones, there is an issue that is not solely down to the tyres but a combination of factors...
We've agreed the Bridgestone tyres aren't great.
Have you tried reducing the tyre pressures a little to see if that helps? With the stiff sidewall - which I think along with the compound is the issue here - running them at the same pressure as the much softer sidewalled PS3 (or whatever) would seem illogical. Reducing the tyre pressure will allow more sidewall flex, generate more heat as well as increasing the contact patch slightly.
I'm not suggesting much, no more than perhaps 3-4 lbs/sq inch...