That's my typical setup right now. Asics running shoes with custom hard plastic arch supports that I've had for ~15 years and wear all the time. Adding toe clip pedals or Hold Fast straps might work just fine.

Actually rode my Peugeot Road bike for a few years with toe clip pedals before switching to clipless. Never did like the stock toe clip pedals, the straps were a very stiff material. The current ones look much more compliant.