The 7 round limit is only for 22 cals. Anything bigger can run a 100 round drum if you want. The caliber in question would be illegal because it's too small. 22 cal is the minimum.
This^^^^
Doc is spot on right here.
The idea of sticking a rod in the mag probably won't fly. Yes I know shot guns use plugs and it's the same concept, but anything that can be altered in the field is usually a no no. It's better to find a permanent fix for one of you mags. But being under .22 cal it's a "no fly" anyway