I experienced the same problem early on in my flash steam project.
I wanted to burn L.P.G originally so I set up a roaring type burner and a copper gas tank with the burner firing into an A.A. Rayman design boiler.
The burner had a .025" jet and brass vaporiser coil on the end.
Before setting it up with the boiler I tested it just as a burner on the bench, heated the coil with a plumbers blow lamp, as I was burning liquid, coil getting a bit red, opened the liquid valve and away the burner went.
Great I thought it's burning well, after a few minutes all hell broke loose as the liquid came shooting out of the burner like a flame thrower and set the inside of the garage door on fire, quickly shut down the valve and it was fortunate that it was a flash fire so no damage done, C.O. 2 extinguisher now installed at bench.
When installed in the test boiler it worked well but was inclined to flame and then would go into the cycle of cooling and losing pressure due to the size of the jet and the amount of liquid being drawn from the tank, heating the tank with a gentle application of the plumbers blow lamp increased the flame strength.
The burner seamed to work better when firing into the boiler space, possibly get more air sucked in, with the occasional flame out from the boiler exhaust.
Eventually I deduced that to get the power from the L.P.G. I would need a massive tank to supply the burner and stop it freezing, went on to paraffin.
Where does all this lead to your problem.
The out side temp of the tank is one, looking at your burner , is the tube too thick to allow it to glow hot and vaporize the liquid?
I found that the outside shell works better at .025" thk.
Do you still have so much tubing in your coil which could be preventing combustion ?
I found that the more space around the coil and the coils spaced about 1/4" apart was about correct, but then my aim was for power that your coil can't produce.
No doubt you will solve the problem when it gets a bit warmer.
Here is a pic of the experimental burner and A.A.Rayman boiler, burner is now fired by pressurized paraffin, this was an early experiment before my final
Hope this helps.