One observation: This carburetor I am working on is a spare, meaning- I have a 'good' one. I recommend a practice attempt with these inserts on a similar material or similar carburetor body before moving to the actual unit under repair. For a 10-32 thread repair, to insert a 10-32 screw, you will be tapping with a 13/64" tap. If this is confusing, try to tap a 10-32 hole that is stripped- using a 10-32 tap...
An explanation of the measurements in the photos:
The screw thread length to be inserted through the carburetor bowl cover assembly, and into the main body is
0.4785" (measured with lock washer installed) ; subtract the carburetor bowl cover assembly thickness of
0.2495", and we are left with 0.2295"
The 10-32 Heli-coil insert is
0.1815".
I drilled the 13/64" hole to just shy of the
0.454" existing hole depth. For a depth gauge, I measured the tap thread exposed prior to running the tap
(0.8765") and measured until I was close to 0.25" depth:
0.629" (to insure the 0.2295" of screw thread had somewhere to go). The 0.25" depth I was aiming for is my calculated estimation of what the "not going too deep" Jon/Carb King mentions, is.
0.8765" - 0.629" = 0.2475" on the tap depth, so I was a little off. This is plenty of depth for a 0.1815" insert, and 0.2295" of screw depth, either way.
Hope this helps. Edit- I forgot about the gasket thickness...

Brad