I see it as totally workable if certain conditions are met.
1- the toe clip has to be slightly too long so as not to interfere with engaging the cleat, and not to pinch when clipped in.
2- the straps need to be kept loose enough to allow unrestricted rotation so the cleat can disengage properly.
It does make disengaging a bit more complicated, and I wonder about learned habits for disengaging if switching back and forth regularly, but the OP can set it up, and give it a go.
I don't worry about how period correct bikes look, but it could be nice to have a bike suited for quick errands and regular sport riding without making any changes except my shoes.
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