Improving LT Spice DC sweep convergence time
When you hit escape during a stalled DC simulation in LTSpice, the simulator progresses to the next solution method. The first method is direct Newton-Raphson iteration. If that fails, LTSpice will try the following strategies in order by default:


Adaptive gmin stepping
Adaptive source stepping
"Pseudo Transient"


From your screen shot, it looks like you are still hung up when you get to adaptive source stepping. My guess is that when you hit escape at that point, you progress to the Pseudo Transient method and get convergence relatively quickly thereafter. I see this a lot.

If you know which method is converging well for your circuit and you are confident in the results, then you can avoid baysitting your sim by presenting .options directives that disable the methods that are bound to hang up. From the LTSPice manual, the specific directives are:


  Direct Newton Iteration: .options NoOpIter
  
  Adaptive Gmin Stepping: .options GminSteps=0
  
  Adaptive Source Stepping: .options SrcSteps=0  
  
  Pseudo Transient: .options pTranTau=0