Seeing as nothing else has changed in this setup except the ground idea, then I agree that the ground you mention is probably a bad idea. I find it hard to imagin the success of soldering a #4 copper wire to the shield of the coax without causing a lot of heat. It can be done, I'm sure, if you are really good at soldering. This probably was done outside at the antenna and that too can make soldering difficult. You may have well cause a serious impedance bump in your coax and maybe that is why the amp is not loading well.
If you wanted to do the copper wire to the ground, then a good physical connection to any part of the base of the connector or to the mounting bracket of the antenna is at the same ground potential as the shield should be at that point. Just keep it as far away from the radials as possible.
There are considerations to be made, but normally the supporting mast is adaquate for making a safety ground connection to earth. It is not the path to ground with the lowest resistance, but if lightening hits the antenna that dinky coax sure aint gona take it to ground before it explodes into space. That still leaves the mast so just use it to start with.
If you wanted to do the copper wire to the ground, then a good physical connection to any part of the base of the connector or to the mounting bracket of the antenna is at the same ground potential as the shield should be at that point. Just keep it as far away from the radials as possible.
There are considerations to be made, but normally the supporting mast is adaquate for making a safety ground connection to earth. It is not the path to ground with the lowest resistance, but if lightening hits the antenna that dinky coax sure aint gona take it to ground before it explodes into space. That still leaves the mast so just use it to start with.