I don't know about that one, but I have the Bosch pole and the Bosch GLL3-330CG laser level, and it comes with a 2-piece adapter that has up/down adjustment on the adapter. We had the same issue at first with putting the horizontal line near the height point then (while on unlock) using the knob to up/down the laser level to that point but when you let off to lock it, it would always settle and move a little bit and not be on point. We found that if you keep the adapter on lock instead of unlock, you can up/down the laser level to your point and let off the knob and there was no settle and made lining up so much easier and less time consuming. It works really nice when you put the laser level where the line can hit several posts or piling from one spot and then hang a long run of girders or joists without having to use a level or even worse using a string level. But the drawback with the Bosch pole is it doesn't have a tripod base so that means you need something above the pole to extend to and lock the pole in place so you can't use it outside if there's nothing above the pole. You could easily bring something with some weight and tie the pole to that object and that works fine but that's one extra thing you got to do if nothing for the pole to fasten to above.
About that mount for the laser. If you use the existing hole 1/4-20 right next to the 5/8-11 that you put your converter into, then it would still be flat underneth.
A good tripod needs to be able to adjust for unlevel ground. I used a photography tripod for that, but it didn't have enough height, but i already had it. For indoor use, you could get away with a shower caddy pole with adjustable height to lock to the top and bottom surfaces, perhaps buying two to allow for high ceilings.
Thanks Matt. I have been through all of the same issues you mentioned with the 3rd Hand pole. I found the Johnson laser pole, which is exactly like the Firecore, at Lowe's for the same price.