Lets see if we can repair this push broom / handle

[RJSakowski]

Not quite following you with everything. Here's a top view of a rough mock up of what I think needs to be done.
The top of the picture is the furthest from the operator. The bottom is the closest to the operator. The left side is towards the head stock. The right side is towards the tail stock. The compound is magenta. The acme tool is green. The work piece is grey.
View attachment 509211

Rotate the compound 180º so the crank is to the front. Turn your QCTP 14.5º, cutting end towards the headstock and positioned as far to the rightas you can.. Regrind your tool with the right side, as pictured above, is not beveled and the left side has a 29º bevel and set in the tool holder with minimum stickout This rotates the tool holder away from the spindle while still maintaining the correct tool orientation. This should buy you the necessary clearance to cut your 3/4-5tpi Acme thread.

 

[RJSakowski]

Here is a photo of a simulated setup on the 602. Angles are approximate. I blackened the 3/8" bit to simulate the tool geometry and there is a 3/4" dowel pin in the chuck. There is about 1/4" of clearance.

 

[WobblyHand]

Here is a photo of a simulated setup on the 602. Angles are approximate. I blackened the 3/8" bit to simulate the tool geometry and there is a 3/4" dowel pin in the chuck. There is about 1/4" of clearance.View attachment 509219

I'm going to say, I hadn't imagined that! Maybe I can make that work. Not looking forward to grinding another tool however, the last one took 2.5 hours and it was noisy. Had to stop and put on hearing protection. Wore out a ceramic grit belt and it stopped cutting. Never seen that before on HSS. Changed the belt and it seems that by the time I finished, it wasn't cutting as well as it used to.

I'll see if I can fit everything in place. My part has a shoulder by the chuck so tilting the tool holder may prevent getting close enough.

Thanks RJ for the suggestion and especially for your effort of mocking up the photo, it is greatly appreciated.