What current rating does my kickback diode need to have?
You have to meet all your diode specifications, average current, peak current both have to be met. Neither is more important than the other, though in a specific application, it may be one or the other that fries the device.

You need to meet average current for average dissipation and so case temperature rise.

You need to meet peak current for max die current, max bond-wire current, and maximum pulse temperature rise of the die above its steady state 'running' temperature rise due to the average current.

Looking quickly at your application figures, 7A at slightly less than 100% duty cycle (delivering very low voltage at stall) looks like it exceeds your 5A average rating. At low case temperatures, and with a generous spec by the manufacturer, you have got away with it. 11A versus 125A will certainly be OK for peak (as long as you respect that 8.3mS time limit, you saw that, didn't you?)

In your shoes, I would be grateful that I'd not blown anything up so far, and choose a beefier average rated diode for production / long term use.