Mud daubers are terrible about plugging up little holes.

Sometimes a piece of weedeater string will fit down into the pee hole and clear the obstruction, but by the sounds of it you have quite a bit of it in there.

I'd pull the thermostat and screens in the lower unit, then stick a garden hose in the thermostat hole and flush the motor from the top down, before taking the foot off. You'll have the best chance of dislodging anything this way.

Those Mercs have a splined shift shaft that is generally easy to deal with, just pull the half dozen bolts out of the lower unit and drop it, putting it back in can be tedious as the water tube, shift shaft, and drive shaft need to be lined up. Some prefer to put the motor in forward gear before dropping it, that way you can spin the prop while lifting the leg, helps line up the splines.