If the wheel fits the same way when reversed its gotta be the frame.

There is a tool to make the dropouts square to each other, a tool to align the dropout hanger, and a guide to lay on the side of the frame to check rear triangle vs the head/seat tube (which is what the string is doing). All worth having; maybe run the frame to a good bike shop, they should have the tools or an alignment table.

If you have someone to help, or have some clamps, run a rigid rod or straight edge from head tube to seat tube inside the dropouts and measure from that.