I would consider giving Direct Line a call. I managed to get insured when I was 23 on my Elise for a very good price.
They are by far the best insurer I have found yet. In addition they will quote you on the Mini with conversion if you state the percentage of power increase on the engine.
I think i paid an extra £20 for my 135 upgrade, (about 15% increase in power).
Good luck!
