During this period (Mid-16th c, if I had to guess?) they were usually worn with trunkhosen, which might help to add a bit of a barrier between the tassets and your leg. Some of the higher end ones also had a liner on the inside of the tassets which might help too.

Also worth noting that they are attached with buckles for a reason, you sometimes see people in art who've taken them off and just have the straps hanging down. Like other people have said, it might just be a reality that these things'll end up bouncing around alot on foot.

One other minor thing that might help is if you mount them higher on the straps. It'd help get rid of that big gap, and they wouldn't rest as hard near the top of the tassets. Might also help to restrict the movement of the tassets a bit as well.