Instead of eye-balling it... here is the field with two 100x100 foot squares. I reckon you need at least 100 feet on each side to play. The bases are 60 feet, and this gives you 40 feet of outfield before hitting a home-run over a fence.
As you can see, you can position these any way you want... but you can't get away from having part of the base paths in the clay. I don't think there's anything wrong with running bases in the clay. But... I think your drawing was a bit too off-scale.
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