You might look more carefully at what the basis for the contact
rating is, and whether application is different. For example 3A at
85C might let you be OK at 10A, 40C. Or something. I imagine
that aged contact resistance times I^2 melting the body may
be the prime failure mode, but you'd have to do the digging.
The right answer might be to not use skinny little signal
connectors to do a stout binding post's job. Not only the pin
current rating, but also the PCB traces leading to it need to be
checked for true current carrying capacity. And for non-end
connector pins that will be a "neck" for sure.