https://reprap.org/wiki/Wire_termination_for_screw_terminals
The terminals in question do have a flat pressure pad, and are tin plated. There is a mains voltage terminal and a control terminal. Both of these are meant to be used with solid wire.
It's clear from inspection that solid wire does not contact the terminal pads very well. Round vs flat, so you get limited contact. There's limited torque you can apply, so you aren't biting into the wire much either -- only enough to prevent pullout. This is a high quality product, so that must be within the design spec.
Does the flat pressure pad snugly fit the slot and have a downward bend at all 4 corners? If this is the case, the terminal may be designed to accept two wires, one on each side. You'll have to consult with manuals to determine if this is the case. In those cases, you don't need to make a U hook. Just straight wire will do. That little downward bent will help with fraying of stranded wire, too.
As to solid wire not making good connection, it's been this way for many years. Even 100 amp circuit breaker is made this way. I think you are over thinking this. I will not suggest flattening the wire either. You'll just make a weak point for wire to break. There are manufacturers of terminals that writes in manual AGAINST using too much torque, as it will squish the wire and possibly damage the terminal.
As to compression wire end terminals, please note, insulated type is for stranded wires only. You will not get a good crimp on solid wires. (even if you use expensive manufacturer supplied tools) Quality of crimp, if you choose to use them with stranded wires, depends on use of proper tool. Too much or too little pressure can cause eventual failure.
If I were to do this, I would use stranded wire larger than spec calls for, and crimp an insulated Y terminal with approved tool. Another way I might do, assuming it is not subject to vibration, is use a solid wire, make an U shape and torque appropriately. Then bundle the wire for extra measure.
FYI: I'm a licensed electrician (but license is from Japan, so it's not valid in USA)