Any tricks to remove drivers from a (sticky) cabinet

you can use a small inside caliper, into screw hole, expand tips and pull from the screw holes, not the edge.

$12. be there tomorrow

or improvise to pull from the holes, not pry the edge

using alcohol, you need to position the speakers to control gravity, i.e. fluid flow. you can lay the cabinets on their back, so fluid won’t run down the face, get an artist’s little paint brush or ... and try a spritz of alcohol, start swishing a bit inside the screw holes, wait a while, then tilt to use gravity to control the flow of fluid, some from the outer edge in any small crevice, bit by bit...

When I upgraded the drivers in my Alon speakers years ago, Carl Marchisotto recommended I use a certain sized screw that was just bigger than the hole in the driver, which was screwed into the front mounting hole of the driver until it became engaged and then I was able to pull the driver out from the front, similar to what was recommended by @elliottbnewcombjr 

I suggest trying the recommended methods posted below before prying against the cabinet, which seems to be asking for trouble.

This video shows a good way to remove woofers from the front:

One way to make this slightly easier is to heat the speaker just a bit with a heat gun, but, I think the approach shown in the video is really the safest.  You have to find the right screw to fit the driver hole, but, that is the only tricky part to this method.

I sympathise with you,

All I can add is to be extremely careful as accidents can happen so easily and a damaged cone is something to be avoided.

As suggested an oversize screw could be worth considering but again take extreme care.

The newer screw heads that take hex drivers are far safer than a Phillips-head screw or the dreaded slot type. The hex fit snugly and are held in place so accidents are unlikely.

A bolt that just fits in the hole could work as adding little angle might be enough to break the seal.

 

If your speaker cabinet is a sealed box, unscrew your driver and play low frequency signal through it at high volume. It may pop the driver off. If it’s a ported speaker, try blocking off the port until it’s air tight before applying signal. Works like a charm if driver isn’t too tightly seated.