I've got Bridgestone one end of mine, Continentals the other -well, I did until the weekend, as I fitted the winter tyres - the same all round now. As I don't tend to drive on the limit of adhesion all the time, I can't imagine there is any practical problem. 22 years of Lancia integrale ownership, couple of hundred thousand miles, hasn't so far shown any problems either - and in the early days of ownership, being skint, there was a different make, pattern etc on each corner, never mind each end!
I would suggest tyre diameter difference is more important - and it doesn't sound like your old ones will be too different to the new, so again, not too many problems I would have thought. It's not got locked diffs front, rear and central, so unlikely to suffer transmission windup.