Any Italian car made before the mid-90ies has this issue, and the older they are the more problematic it is. I'm 6'2" with relatively long legs, and I have this problem to a lesser extent but it is still very noticeable.
Personally, I have found that spending a little time in finding a position with splayed legs gets me comfortable enough to drive the car without being constantly annoyed. I had a 1982 Alfa GTV6 which had this problem in spades (with a very heavy clutch to boot) but driving it daily didn't phase me. The 328 GTS of my brother had it a little less so, but still it was tight.
I know a guy who's (I'm guessing - he's definitely taller than I am) 6'4" or 6'5" who owns a 1977 308GT4 and he takes it on 7 - 8 hour trips through Europe. He doesn't seem to find it a problem at all.
Bottom line: for a reasonable fit you need a F355, 550, 456, or something more recent than that (my 550 fits like a glove, I don't even have the seat all the way back. You would fit in without any issue). These cars fall outside of your budget. If you want to drive a Ferrari for your kind of money, you're going to have to accept a more awkward driving position.
Regarding modification, I can't help you I'm afraid, but it seems to me it would be quite expensive. I don't think you can move the bulkhead as the engine would be in the way, so the only solutions I can think of would be a Gurney bubble or a lengthening of the chassis. Both would be prohibitively expensive, and severly compromise resale value.
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