On every vehicle I have ever restored, there is always at least one item that is made of either unobtanium or verypricium. You just found that item on your vehicle.

Options (probable cheapest first):

(A) replace the transmission
(B) replace the Stromberg with the Carter that was also used
(C) buy a new solenoid

Carter used a different solenoid, and they are at least reasonable.

Jon.

Good carburetion is fuelish hot air
The most expensive carburetor is the wrong one you attempt to modify.
If you truly believe "one size fits all," try walking a mile in your spouse's shoes!
The Carburetor Shop