I need a handful of .45LC cases machined with a deeper and wider groove above the rim for test purposes.
Been trying to get a Chiappa Spencer reproduction to cycle reliably.
I believe the issue can be solved by a deeper groove for the extractor hook.

Is there a place I can get some custom machined cases done?

Have you considered altering the extractor to work with the SAAMI spec's for that caliber... rather than altering SAAMI spec brass?

Modifyng the extractor will not work.
The extractor doubles as a cartridge stop for the round feeding out of the magazine on lever opening.
If trimmed short enough to work on extraction it allows override on the cartridge causes jams.
The problem is the extractor makes an upwards movement before it begins it rearward movement.
When a cartridge has been fired and the case is fully expanded the extractor contacts the rim and essentially locks in place.
Forcing the lever causes the breachblock to fly down and out of the receiver. Cartridges spew out of the mag tube. The gun must be disassembled and reassembled.
Unfired cases have enough room to move in the chamber to allow the extractor movement to work normally.
Examining the original Spencer rifle and ammunition makes me believe this upwards movement of the extractor is a design feature to insure a gouging grab on the rim of the original thin copper cartridge case. This was done to insure extraction.
The modern reproduction does this as well but the much harder brass case doesn't allow the extractor to cut into the case.

So my thinking is to deepen the groove slightly to allow to extractor its full upward movement.

I chucked cases in a drill press to deepen the groove once.  Just used a file. 

I would just use a stone on the extractor until I could get cases to cycle.
The above sounds like a fitment problem.