Inletting that breech and tang can be aggravating for sure. From your photos, I can see that the tang is humped up too much. I would do as your previous advisors have suggested...but I'd soft solder the tang to the plug, ONCE IT IS FIT PERFECTLY. Then I'd take a little of that hump out of the tang just back of the plug, and see how it fits into your stock. You can always inlet the tang into the wrist a little deeper, but you likely cannot move it back...more gaps will show up where the waist narrows in the back end of the tang.
Once that is all done, if there are gaps, bed the breech with AcraGlas from Brownell's. Use a tooth brush to apply shoe polish to the assembled barrel, breech, and tang, let it dry, and lay in your AcraGlas. Colour it with some of the brown dye, and a tiny bit of the black.
A note on your hooked breech. There can be no play fore and aft. The hook must hold that barrel securely, or it will bounce forward on recoil, and increase the play in the metal to metal. Also, accuracy will be lousy.
Hawken rifles are fun. I've built close to two hundred of them over the years, and swore I'd never do another. 'Til I built that full stocked rifle for Hatchet Jack Bradford. Now I have all the stuff together for a half stocked .62 cal for m'self. They're beautiful in their own way.