I suffer the same problem when I ride my DF's. I now do my recreational
riding (non-commutes) on a recumbent and find I can ride pain-free all
day long. That does not however mean you need to change to a recumbent
yourself, as many folks on this forum who are wiser about these things than I
have successfully beat the neck pain thing with stem changes and bike
adjustments and such. I just didn't have the patience to deal with all that, and I
had always thought recumbents were Cool, so that's the route that I took
to aleiviate the pains associated with cycling.
I'm confident the folks here will steer you in the right direction.