How do I go about finding a stronger spring?

Take a look at the link in the first post, or better yet, here’s a short video of one being run through an entire cycle.
The handle to raise and lower the door isn’t any kind of a lever or anything like that*, it’s just a grab handle to lift and/or lower the door with. It’s like a handle on a window (and, come to think of it, window counterweights were what I was picturing).
*It also happens to be a safety, but that’s neither here nor there.

It’s a little tough to do with a hand held drill but it wouldn’t be too tough putting a 1/4" hole for an eyebolt in that back plate if you use a carbide bit and some oil. Titanium alloy and those type won’t get you there though, got to be carbide.

And you should do some welding. Welding to that heavy plate might be a little tricky, especially if you have to do it in place, but you should do something just for fun anyway and maybe you’ll end up welding something at work. At least something like that doesn’t need the best* looking* welds.