This is one of those times, where a precise RD isn't needed, since a Shotgun isn't known for being a precision type Gun, but you needing a RD that's built like a Tank and can take the abuse.
I don't know anything about the Burris Fastfire models. I have a couple FullfieldII Burris Scopes and they're built very well, but I don't know about their Red Dot counterparts.
I have a Tru-Glo model on a little 9mm Carbine and it's worked very well, but a 9mm compared to a 12ga. Just don't know if it'll last long, but who know unless you try it.
What I have on my Turkey 20ga, is an older Bushnell Trophy(long tube) 4 Reticle Red/Green Scope. It's taken a beating for last 3-4yrs and done really good.
Primary Arms, AimPoint Pro, Bushnell Trophy, Mueller, Weaver, and Leupold, I know all make some good Red Dots, with prices that might work. There's many others also.
Honestly, I would call all the Manufacturer's that you might find a Red Dot from and point-blank ask them if it will stand up to a 12ga over time. Also remember, that some also will Warranty the Scope for Life, BUT the Electronics will only be Warrantied for 90days or so.
If this doesn't work, also look at SWFA for a RD Scope choice from the Manufacturers. You'll find some from $20 all way to $3000+.