I can only add my opinion to this thread, based on my own experience, and I feel its very relevant to your problem.
I bought my Zed last November and I had the exact same problem... the dealer put brand new tyres on the rear when they serviced the car. Obviously when I collected the car I thought this was a good thing, two new tyres thrown in the deal! Too good to be true? Well, yes, as it turns out.
I went through the winter wondering whether I'd done the right thing buying the Zed. Surely this car should out-handle the Celica it replaced? But I had to be soooo careful through corners if there was any hint of wet (remember this was November/December) and even accelerating. For example, there's a junction I pull out of every morning coming to work and on both the 2nd to 3rd change AND the 3rd to 4th change I had to be careful... too snatchy on the clutch and hard on the throttle and the back end would twitch and the traction control cut in. To be honest, if it weren't for the traction control, I reckon I'd have been in a ditch over the winter.
I got the money together and decided to gamble... a set of Vredestein Ultrac Sessantas all round. £640 fitted.
Even before the tyres were scrubbed it was like I was driving a different car. A thousand miles later and I have SOOOO much more confidence in the car and am getting a LOT more enjoyment from it. The Zed feels so much better balanced and composed. It turns in sharper and I get better feedback. I'm back to grinning as I zip through corners.
The difference for me was quite pronounced. I had Bridgestone 040 up front and some cheap brand on the back, so pretty dire. No doubt on some combinations you can get away with mixing tyres front-to-back.... BUT... the point is I don't know why having all the tyres match makes a difference... I might be able to offer some ideas about mixed compounds and tread patterns and what the electronic bits are getting told, but ultimately I don't KNOW. And I think there are very few people on this forum, if any, that can really claim to know 100% of the science behind the grip that keeps us on the road... and THAT is the reason I think we shouldn't mix tyre types across the axles... it is the ONLY way you can be SURE that you're setting the car up as well as possible, and in the way the car was designed to be driven. It takes a lot of arrogance to claim otherwise!
Whatever your experiences to date, I hope you'll consider that view.
Do you want to drive your car fast through a corner thinking its "probably alright" mixing tyres across the axles, or do you want to know you've given yourself the absolute best chance of maintaining grip?
Frankly, I'd rather trust the engineers and designers of the car than myself.
If none of that convinces you... I'm pretty sure that one factor the car uses to judge whether the traction control should cut in is the difference in speed between the front and rear axles. Logical really, isn't it...?
Whatever you decide to do mate, I hope you get the car sorted out and can get on with enjoying it