Success!
I fixed my laser!!! Finaly..
After discovering, that the beam varies the most with pressure on the button, i unscrewed the battery compartment, and looked into the laser module..
I noticed, that the spring is not in the middle before, but i didn't pay too much attention to it. This time i noticed, that it's moved more in the direction of the pressure on the button..
I removed the foam, that is hiding the "driver" board, and noticed, that it too is much closer to the opposite side of the laser body, and when you push the button, you just push it in that direction even more. There is a big transistor (or IC) on the other side of the PCB (opposite of the button) and it's only supported by a few more pieces of foam.
Since the "driver" board is directly soldered to the legs of the IR LD, every time you push the button you put strain on one of the most sensitive parts of the laser!
I decided to put a hard piece of plastic below that big transistor, so i cut two small rectangles from a 1mm thick plastic board and glued them together. Then i used a screwdriver to push the PCB up and put the plastic in place under the big transistor with tweezers.
Now the board is supported much better, and can not move with pressure on the button anymore. The spring is also closer to the middle...
I put the foam back around the spring, and put the batteries in. The behaviour of the laser changed dramatically!
Before, it liked being cold, started very bright, as one beam and mode hopped when warm, losing brightness.
Now it starts as two beams, but they immediatelly start joining, as it warms up, and turn into one beam in just a second or two..
Before, the longer it was on, the worse it got.. Now, the longer it is on, the better it gets! It gets to full brightness in just a few seconds and remains there! The abrupt brightness variations are also completelly gone! I tried with several different voltages and the behaviour is FINALY constant, as soon as it warms up.
Now i am happy with it.
One more thing.. Even if it worked perfectly all along, i would have prefered to have the PCB supported, so that pressure on the button can not break one of the LDs legs away..
I also think i know why most people get better results with Ni-MHs. It's possible, that rechargables are slightly longer or shorter and put a different pressure on the PCB through the spring.. I don't think it has anything to do with voltage or current anymore, except being somewhat related to it through the heat the current produces, and the resulting deformations inside, combined with button pressure variances.
The manufacturer should really build some support for the board under the button into the laser. It could be so much better if only it had this piece of plastic inside already..
Oh, i also just remembered the reason, the board is pushed so far down. There is another spring inside, going from the LD + up to the body of the laser, to provide electrical contact. This is what pushes the PCB down, and combined with pressure on the button and heat, causes the laser to malfunction.
It's a major design flaw, and all that's missing is a piece of plastic....
EDIT: I just wanted to add, that this fix, while it worked for me, could theoretically make things worse for someone else.. It might still be usefull in the long term, to support the PCB from below, but if everything works fine, don't bend it up like i did, just support it (so pushing the button doesn't cause strain on the LD), or do nothing at all.
Just gently supporting it on the other hand, could prevent it from developing this problem in the future...
