(Hi Victor!)
With regard to tuning of a gantry setup, I've given it some thought, so here's my 2c worth.
With your bridge off, if you can come up with a plate or other mass you can bolt to one of the bridge base drives, that is half the mass of the gantry, then you can tune it up and copy the file to the second amp and continue on.

Obviously though, you must have your mass attached well, so there is no flopping around or other erroneous motion just from the mass during tuning.

For squaring using only Quickset, I can't think of a good way after power-off other than throwing a square down and using an indicator, and jogging one till it's right.
If you're using Control Point, it's much easier, as the two axes' position indicator goes green when crossing the index channel on the encoder, telling you the count that it occurs. Then, when you know you are square, you need only to record the count difference from indexes. Next time, jog one till it's the right offset.

Otherwise, I'd make some precision blocks in place of your hardstops that can enforce the squareness, pull the bridge to these stops, and enable.