Old size Tires (50's) vs Metrics of Today

[Jwawhite]

My original tire size is 7.10 15-4 according to Shop Manual.

This translates over to: P215/75 R15.

The spare tire compartment is in the rear of the wagon covered by a lift up door.

The issue is the width of the tire near the top of the sidewall, it's too wide and the tire needs to be deflated to fit. Ok and not ok.

The old tires didn't they have straight sidewalls w/o the bulge of modern tires?

Is there a work around other than buying an expensive Cooker or? It's just the spare but I'd like it to fit better.