For the IIe's (4xPlatinum + 2 regular) I'd recommend the built in self test (assuming the RAM is in reasonable condition.it will run) - Key sequence is Control, Open Apple, Reset. It will test the RAM and some of the key custom IC's.
The 2 Europlus are a little more tricky due to the number of chips - I'd start with reseating all the IC's and then removing everything but the 1st bank of RAM.
Obviously before starting these computers up make sure you take care of the RIFA caps in the power supply.
As you have discovered you will likely struggle to load software directly into memory if there are any faults with the computer. You can however try places like this https://asciiexpress.net/diskserver/ which have a range of software setup for audio delivery. I didn't see any test software. Obviously ADTPro with a disk drive is your best option.
Cheers