Well, I would say it boils down to this: how can you achieve usable data from HFSS with a minimum number of points or tetrahedra? You can take your existing model, reduce the mesh size and compare the data to previous HFSS data with a tighter convergence. You can do that by reducing the maximum number of passes or increasing the delta-s criteria (yours is currently set to s=0.02 - try using 0.03). Try it to see if it works for you. But, at some point you'll just lose accuracy - and that will turn into wasted time. But, it's still worth a try. Compare models using less points to those using more points. I wouldn't use a single comparison, but a few to get an idea. If you feel you can live with the error (or can't tell the difference) - the continue with less points.
Also, there are steps that could reduce the model size. Although, I don't see symmetry right off the bat from your model - people have cut their physical model space by half using symmetry. If you're solving the inside of metal then you'll get a warning that this will use a lot of meshing points. For your project don't solve inside metal (that's the default setting anyway). It's physically large enough that you won't need to solve inside metals or other highly conductive objects. A PML boundary might be better for reducing the number of tetrahedra. Occasionally, imported objects can create unnecessary meshing points due to imperfections in those imported models (such as small hard to see gaps or slight misalignment). You can view the mesh in HFSS and ~sometimes~ you'll see something obvious. But, I can see you've generated the helical using one of the scrips within HFSS - and did not import anything - so I really wouldn't expect that to be a problem.
What is the size of the air cylinder with the radiation boundary? Can you change that to PML and reduce the volume?
Also, I've heard of software packages designed for antenna simulation only - they may be far more efficient compared to a more generalized finite element method.