What was the solder that you were originally looking for?
Amscope do articulating arms btw. But to get more space see if the stand is reversible and clamp it down to the edge of the bench, might pay to remove the microscope to avoid toppling it over while trying.
If that works then you could possibly make up a heavy duty right angle bracket, mount it securely flush against the side of the bench, then mount your stand. You could bolt everything down so no accidents.
A flexible right angled HDMI cable might be better so you can secure it to the microscope without causing strain on the port. A right angled extension cable for the ring light would be better as well (or just replace it if it sucks).