I wish mine would just twist off, lol
I hope that when you were cleaning it that you were holding the barrel and FH and not the handguard/upper and FH. You are aware that you can twist the barrel in the upper that way?
If that is the case then back to springfield you go

When i started to get fliers with my 15-22 i got the barrel nut tool and tightened it up, it only took a little bit of movement, it was certainly not 'loose' but my accuracy and groups got a lot better after i tightened it up.

To be missing the target with a scope, seems odd, i hope you have not twisted the barrel in the upper.