I have a shotgun barrel (Beretta 1201FP) that the solder holding the barrel lug on has failed.  
Is soldering this the best attachment method, or is there an newer epoxy type connection that is worth looking at.  
If soldering it is, with the gunsmiths backed up with months of work, is there a method to DIY this fix?
Thank you in advance for any advice.

Good luck. A friend had a Remington 1100 the barrel ring became detached. We tried and tried to solder that thing back on w/o success. Even bough a paste to insulate heat from the rest of the barrel.

Thank you.  I have a better list to call now.  This is excellent.
I forgot about Midwest, the others I did not know about.  
One shop I called did not respond at all, the other told me 4 weeks for an appointment to bring it in for the quote!!

Another vote for HF44 or similar. You don't want common "solder" - you want silver solder/bronze braze/silver braze and a good flux. Any should work for this project.

Doesn't take much either but you do need to scrupulously bring both surfaces to bare metal first.

Another option is the famous Nu-Line Guns now in Rhineland MO.

http://www.nulineguns.com/profile.php

Nu-Line has been around since the 1940's and for years was in the St Louis area.
For most of that time they were a gunsmithing business, and as I recall, during the Vietnam War they had a contract to build M14 barrels.

As mentioned above, shotgun barrel supports are BRAZED on with a high temperature brazing alloy.  It can be real silver solder or other compound that melts above 1100 degrees.
NO soft solder will hold, including the 3% silver content soft solder sold in hardware stores.

Due to the red heat needed the finish will be destroyed so the barrel will need to be refinished.

Another, possibly even better option would be to send it in to Beretta USA and have them repair it.
A major problem with replacing barrel supports is that the support HAS to be perfectly centered or the barrel may not fit on the gun, or pressure can cause it to shoot off target.
As example, Remington uses a special barrel fixture when brazing on a support ring to insure it's perfect.

Beretta has service centers around the US but I'd send it to Beretta USA.  Since it's just a barrel you can ship it cheaper then an entire gun.

https://www.berettausa.com/en-us/customer-service/find-a-service-center/

I just resoldered a Norinco 870 clone.  I've done a few different barrels, all the same, clean it clean it clean it.  I tin both sides then clamp together and get em hot.  I use an old roll of 1100 degree silver solder from Brownells.  The tape type makes the process a little easier, but again, CLEAN it.    

yep........many solder joints fail (or leak) because the work hasn't been cleaned/prepped well enough.