I have T-Rex arms, lol, and I managed on standard bikes but there's a huge difference riding a bike custom fit (I have a Bike Friday). Since my bike is my car as well, I had no problem justifying the additional expense.
I recommend, if your
budget doesn't allow a custom bike, that you spend the $ on a professional fitting. That will get you pretty close to cycling nirvana for a reasonable amount
of money; allow for some new parts (bars, stems, seat/post/cranks) based on the fitter recommendations.