The NEMA classifications assigned to receptacles and plugs is there to help prevent the exact thing your experiencing. Ive had dozens of people ask me to install a receptacle that matches their plug...wont do it. The reason that outlet is embossed with 125 v 30 amp is so no one would plug a 120 volt 30 amp machine in and find out that the idiot electrician attached 220 to it.
I make my clients change out the plugs to match the required outlets every time. if they dont want to, i walk.
So far ive never had anyone say thay dont want me to. they always want it done safely. Also, the NEC doesnt say anywhere that you cant have 2 or 3 or 4 individual 50 amp 240 outlets under the command of a single 50 amp 2 pole breaker. Its done in commercial shops all the time. What is expected is the operators to have the skill level not to overtax the system.
I set up commercial cabinet shops with a table surrounded by 8-10 different 220 pieces of equipment.... shapers,router tables,saws,etc.
All on one breaker. The operator runs the door thru the 1st piece of equipment, shuts it down and starts the next and runs the door thru...etc.
All 100% NEC approved and inspector passed. The main difference is....skill level.
Alot of home mechanics tend to forget what to do after 6 months of not using a piece of equipment and may run both at the same time. but thats what the breaker is for. it trips ( in your case a 30 amp breaker would add a safer level of protection).
As far as circuit size. I usually rate equipment circuits at 125% of listed amperage to allow for start up surges. The cheaper the motor, the greater the starting load tends to be.
Thats why alot of welders have a 50 amp circuit, but if you actually test the line while welding,. it may only read 20 amps. But thees a large starting spike.
In my own shop, i run the compressor at 30 amp breaker... not 50. If my compressor ever trips the 30 amp circuit, then that tells me to check its condition. Its my fail safe device since the motor doesnt have a motor control and heaters.
anyways.thats my 2 cents worth.