This might be useful to Tormek users...
This week I found an effective way to sharpen the inline awl on the 93mm alox models, like the Pioneer.
I've mangled my fair share of inline awls over the last 25+ years. Both while using them, and while attempting to resharpen them, freehand and with jigs... So this feels like a long overdue victory.

I use a Tormek T8 with
- multibase (to run the wheel edge trailing)
- extended universal support (to get the steep angle)
- small knife holder jig (to clamp the SAK's body)
- SG-250 grinding wheel, of which I rounded the corners with a cheap diamond plate (rounded corners to match the round termination of the awl's cutting edge near the pivot)

How:
- adjust the grinding angle to match the existing angle of the awl's cutting edge
- run the wheel away from the edge (edge trailing)
- cut a new edge
- I deburred with a Spyderco Ultrafine triangle stone
- finish with a light stropping (I did not use the Tormek here)
The result looks pretty much exactly like the factory edge, in the eye of this beholder...

I've now fixed the awls on several old cross alox's, and old standard issue Soldiers. So satisfying!