And what happen with your Na, where H coming from
I suggest the path to H3CCOOH and after that:
2CH3COOH + Ag2O--> 2CH3COO:-Ag+
CH3COO:-Ag+ + Br2 --> CH3Br (Borodin reaction)
CH3Br + Mg--> CH3MgBr (Grignard)
CH3MgBr + H2O or alcohol --> CH4...
Also from acetic acid-->bromacetic acid-->nitromethane-->Me-NH3-->Hoffman elimination-->CH4
Do you think bromacetic acid may thermally decompose to CH3Br?
Thats what i can suggest now