I'm not sure why you worry so much about the very end of the ens runs. You know this is subject to larger errors.
I have done some analysis of each of the big 3(GEFS/EPS/GEPS) over multiple consecutive runs(fwiw lol), and I think there is a decent shot at a snow event mid month, +/- a day or so. Building EPO ridge, SW trough undercutting the western ridge with energy ejecting eastward, and a pretty solid look in the NA. All models to varying degrees indicate significant precip in the Tennessee valley with height lines oriented SW to NE. Ofc it might not work out but there is potential in that window on guidance. If it torches beyond that, so be it. As we know, these modeled warmups in the LR have been perpetually pushed back for months lol.