Hello, I can help you with this. You really checked everything! you either have a weak compressor or a gas leak. Did you notice the compressor being unusually hot (like burning)?
How about the discharge line 6" from the compressor? hotter or the same as compressor temp?
You have a leak for sure then, not enough gas to compress.
The discharge line is heated from the compresson, since the compressor is hotter that means that no gas is left in the system.
Usually 5 years on the evaporator (likeliest leak point) I think the cleaning was just a coincodince. The warranty would cover the parts not labor, you could go on the maytag website and find the warranty company in your area, they should be able to get the evaporator directly from Maytag for free for you. They should be able to do an emegercy charge to get you buy till they get the part.
At the very beginning of a turn on you don't have the compressor heat working against you. Once the compressor heats up from the mechanical action that works against you.
Same principal as the fan motor.
You may have to eat fast. good luck and happy 4th. Also you should know you did more checking of components on your own than any other customer I've helped in years.