That type of texture with Timeless using an HVLP is certainly not to be expected. That texture, and the mist coming from the gun not quite being fine like you mention is typically caused by a few different factors: 1) Too high of a coating flow 2) Too low of an airflow 3) Dirty nozzle, or one that doesn't allow the correct adjustment/flow to exit.
Does your PaintZoom allow you to adjust both the flow of Timeless as well as airflow, or just an airflow adjustment? What are these settings at currently?
Does your nozzle allow for a flat fan pattern, or just a cone-shaped mist? What is it set at currently?
Here's the way I typically setup a new gun. Fill the hopper with water and adjust the air and coating flows until when standing about 12" from the print, the fan is about 12" in diameter. Some slight adjustments will probably be necessary once Timeless is used, since it is thicker, but it is a great starting point.
You should be perfectly fine using an automotive-type HVLP to spray Timeless. You'll just want to make sure it's internals are spotlessly clean before use. Also, you'll want to make sure filters are setup properly inline so that you don't get any oil contamination from the compressor. Also, makes sure you drain the compressor tank(s) on a regular basis. This type of gun might actually give you MORE control, since they typically offer both varnish flow control as well as airflow, when many turbine-driven guns simply allow for air control.