Personally, I think long barrels absolutely require at least four barrel tenons. That's way too much space you have between them there. Bedding won't help, as that won't stop the stock from pulling away from the barrel.
First, make sure that your barrel really is set ALL the way down in the channel, and your pins aren't lifting it up. Clamp it down tight at each tenon with the pins out and make sure that your holes are aligned, and your pins draw the barrel tight in the channel. If they don't, then redo the tenons.
Then I would say definitely put another tenon between the two existing ones... and maybe another in front of there too.