I don't own a Milwaukee regulator, but I have several Ideal 52-1-12 needle valves. They have female 1/8" NPT ports on each end which require male 1/8" NPT adapters at each end. The safe way to set it up is to use a 1/8" NPT check valve between the Milwaukee bubble counter and the Ideal needle valve. Between the solenoid and the Ideal needle valve, you can use a 1/8" NPT hex nipple. You can get one at Lowes, Home Depot or a plumbing supply.
These are the ones at Lowes and Home Depot made by WATTS:
No. 122 Hex Nipple
1⁄8" MIP Both Ends
You can get a male 1/8" NPT check valve from Clippard, Swagelok, Parker, eBay, etc. Get a low cracking pressure check valve.
my guess is you'd prob need a new jbj bubble counter, too. The nipple outlet for the gas in that milwaukee bubble counter is conneceted to the needle valve. You remove the needle valve and you have a gaping hole...no fine bubbles just a lump of gas escaping into the bubble counter from the new 1/8"npt fitting and the idea valve...
I retrofitted Milwaukee setup by swapping out the stock regulator with a 2-stage harris and a swagelok low flow metering valve. Milwaukee needle vale is left alone because 1st, I wanted to minimize the changes/cost, 2nd it was a bit difficult to take off.
Heemskn also swapped out the stock Milwaukee needle valve with a parker metering valve.
here is his built.