I think the main issue is the heat transfer vs. how much heat is generated.  Might I suggest a different approach. 

Have a copper pipe sealed to an addition/separatory funnel at one end.  Heat a decent length of the copper with a torch and allow the methanol to slowly flow in.  I do not like the procedure on frogfots page.  The entire apparatus has many superfluous elements for such a fundamentally simple process.  As long as one end is sealed against the separatory funnel, positive pressure should be generated.  Enough to bubble the gas into water.  Might be more advantageous to run the stream through a condenser before hand to eliminate any methanol passover.

I will open a whole threed soon as I want the input of the community before I release my current method for making glacial acetic acid from an (aq)solution of AcOH.

I'll be looking forward to that one!

PP

That's interesting. I would have never thought of it on my own.

In addition to your recommendation, I would think that we might be back to where an electrically heated wire in an environment lacking oxygen might be feasible.

In the method you suggest, BTW, how closely do you think the temperature would need to be controlled, and what would that temperature be?

PP

I doubt it gets turned into acetic anhydride - I think that reaction would be exothermic, wouldn't it?
It perhaps just oxidizes, keeping the Cu red, and producing CO2, H2O, etc with out the flame.