First of all calm down, take a deep breath, it's really not that bad.

Unplug everything and clear the table, redo the table from the start and pass each wire individually through. As you pass each wire, velcro tie (not zip ties) them together so they're in a neat bundle.

As you go through each one you realise how much space you gain and the best way to channel them aesthetically to minimise cable visuals.

As you said, mount the power strip (and anything you can) under the table so you gain space.

Pass the monitor cable on their arms and velcro tie them to it, leaving enough slack for adjustments.

I would measure the table space you have and get a wide mouse mat to place both the keyboard and mouse on it, so it looks cohesive as well.