The problem with multiple entry threads is that for a given TPI, every additional start multiplies the lead angle of the thread equivalent to the number of starts. So if 18 TPI at a specific diameter has a lead angle of 1 degree, 4 thread entries will increase the lead angle to 4 degrees, and you will no longer be able to screw the barrel into the action.
You can counteract this by increasing the TPI. So if you increase the TPI to 72 (18*4=72), you would have a lead angle that's close, but not exact. The minor diameter of the threads on the tenon would be too large and would interfere with the major diameter of the threads in the action. To get the lead angle at the pitch diameter to match up exactly, you would have to thread the tenon at 72 TPI, with 4 starts, and a major diameter of 1.029". I'm not sure if there would be thread interference at this diameter. I'm also not sure if you'd get enough thread engagement at that diameter to have a secure fit. I suspect this number is close but not perfect, some trials in scrap pieces would be necessary to see if this is feasible. The threads would not engage at the pitch diameters on both parts. I'm pretty sure you could get something that will screw together, but strength would probably be considerably compromised. The considerable length of the barrel tenon would probably give you enough of a safety margin that it would still be functional.
It's an interesting machining puzzle, and it would be cool to see. But it seems like the consensus is that indexing is a waste of time. Solving unique problems like this is never a waste of time, in my opinion.
Math skills are not my strong point, I used this thread calculator to cheat and generate some of the above numbers. I probably made some mistakes.
http://theoreticalmachinist.com/Threads_UnifiedImperial.aspx