I responded to your bragging thread post, but then read this. I don't know how well I can explain this, but if we were standing next to the motor I could show you in 20 seconds.
Take a look at this picture...
That's my merc lower unit, and the smaller silver rod on the right is the shift linkage rod. Yours should be similar. It runs from the lower unit up to under the cowling where it's connected to the shift mechanism with a pin. When the rod moves up, it shifts the lower unit into gear (
I can't remember whether up is forward or reverse, but it doesn't matter for this discussion) and when it moves down, it first goes into neutral first and then into gear in the opposite direction. When you reinstall the lower unit, there are some pretty specific measurements for the length of that shift rod, and you're supposed to adjust it before you reassemble the motor.
About halfway up the shift rod, there is an adjustable clamp that engages/disengages the trim lock lever when the shift rod moves up and down. When set correctly, this prevents the motor from flipping up while in reverse. You may have to loosen or remove this clamp to make any adjustments, so just be aware it's there.
Now, I'm not saying this is your problem, but it could be. So, try to picture how the tiller handle rotates and adjusts the throttle accordingly. Well, the shift rod has to be adjusted so it matches the tiller's throttle adjustment. For example, shift rod in neutral position has to match throttle in idle position. If not, stuff like you're seeing will happen. Plus, if it's far enough out of adjustment, it may never move the shift rod far enough to engage reverse.
If you remove the pin under the cowling and loosen the trim lock clamp, you
may be able to twist the shift rod and adjust it. If you can't do it like that, then the lower unit may have to come off. At the very least, you should be able to remove the pin and push/pull the shift rod up and down manually, to make sure it shifts like it's supposed to.