You have the 3C0 version? This is really old and may explain why it only uses GSM mode communication with the SIM card. I didn't mention this in my last post, but usually the Premiums "talk" USIM. I'll have to check that again with my 3C0. Maybe the Three card freaks out because of the ancient GSM mode? Who knows...
You may try to get a device with "DDP" from the list: http://www.android-rsap.com/faq/107.html
. They should all support the red display and especially the 5N0s are quite cheap on eBay because they all don't support the Handsfree profile, which most people prefer. I'd guess you should be able to get a box for less than 20€. I'm not 100% sure that they work in your car, because the 3C0's menu structure differs quite a bit from the later versions.
I don't think the mode switch wil help, this only seems to affect the 3G capable Premiums and the logs look completely different in your case.
I once saw an adapter to make the new "white display" Premiums work in "red display" cars, but it was very expensive, as far as I remember more that 200€. And I no longer remember who made it or where to get it.