Make your own grounding point, but measure the resistance between that point and the battery negative. Not the point where a ground wire attaches to the body and through the wire that can't handle the added current of additional amplifiers, AT the battery terminal. If the battery uses the studs for side terminals, use new studs that can accept accessory cabling terminals, on BOTH positive and negative.
By "solder an eyelet on the ground strap", are you referring to one of the braided connections between the engine/body or at different parts of the body to the frame? Nope- those are bonding conductors- there's a difference.
I installed literally thousands of power amps in cars, trucks, boats, etc- the resistance between the ground AT the amp needs to be less than about .1 Ohms if you want to avoid alternator noise. Also, make sure that ground isn't between other ground points and the battery- if it shares a path with other electronics/electrical devices, it can pick up noise.
If the amp(s) added use more than about 20A, increase the wire gauge for the ground wire that connects the body to the battery- the one from the factory is sized to handle the loads from OEM electrical devices, not much more.