MM V should work with 5 V too.

300 mA are sufficient.

"integrated HG550" means: somebody has modified the module.

We don't know what exactly has been modified.

Possibly the module has be tuned to 10 MHz?

It's difficult to decide whether a board is 5 V or 6 V without opening it.

Best way would be to buy a board from somebody who can open it and thus guarantee for 6 V.

Anyway, it could be, the module is damaged and the problem has nothing to do with board, voltage and current...

Cheers
Andreas