2004 BF200 XA-Installing Shift Shaft in Lower Unit

I got the parts I needed to install the shift shaft in the lower unit and everything seemed to be going well. But as I was putting everything back together, I tried to make sure everything was working properly by attempting to take it in and out of gear and nothing was happening. The more I played with it, I think I figured out that the shift shaft was not engaging with the shift plate coming off the propeller shaft.

I believe the lower unit is in gear and therefore difficult to get the shift shaft with the shift plate just dropping it in from above.

My next step is to take it to a mechanic to get him to take the propeller shaft holder unit out of the foot (I don't have a puller) and put it back together, unless anybody can recommend a way to get the shift shaft to engage with the shift plate, given the situation.

Any thoughts?

Thanks!