Hate to rain on your parade but Gyromite carts with NES gamebit screws will very likely NOT not have a converter in them.
There are two indicators that are nearly 100% guaranteed to net you a converter.
1.) It needs to be a 5-screw, standard screw cartridge. No gamebit screws.
2.) (Thanks to InsaneDavid for this tip) The pin connectors coming off the bottom of the cartridge need to look like this:
Attachment 3726
NOT like this:
Attachment 3727
While there may be examples that contradict these criteria in the wild, the above - ESPECIALLY the chip example is the right way to hunt for Gyromites with converter boards.