Wish we knew more details about your problem. Just what is the "ugly" you describe??
A few thoughts in no particular order.
You really shouldn't have gas problems at the start after your gas system is purged. A few welds should purge your gas system, as would loosening your drive rolls (so not to waste wire) and pull the trigger for 12-20 seconds at the begining of your weld session. Your weld power (contactor) and gas solenoid do operate at the same time. There is no delay between them on the type machine you are using.
Unless, of course, the solenoid is bad and is "hanging up" when power is applied.
Fabricating a preflow control would not be all that difficult.
A delay relay, appropriate pot to set timing, and some wire is all that would be needed. A schematic diagram of your machine would be a necessity.
Another cheaper and easier fix might be-start your arc appx 1/4-1/2"
ahead of your intended starting point. Run back to your intended start area (quickly-to avoid build up of weld metal) and then continue as originally planned. This technique can give some preheat to your start, reducing the mig start "lump" and get your gas going by the time you reach your starting point. It may cause some surface porosity-but that may be better than your original problem.
Also-look at your weld. If you see a tan-brown smoke or soot around it-get another cyl of argon. You may have some wet gas. Not uncommon in cylinders filled in mid-late summer. A loose connection, leaking hose,
etc. can give similar results.
Keep us posted.
Good Luck
brande