I would expect plenty of instructors will fit in around you, doubt you'd have trouble finding one if you just ask around.
I used
On Track Aviation for my FIC, just weekends for the first couple of months. All their instructors are part-time, they have other full-time jobs. One or two of them work Monday-Friday at Oxford, so doing the FIC at weekends fits in perfectly with their other commitments. I have no connection with them other than being a satisfied customer.
FFF
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