"Bonus points" for digging right in there Igor, good for you! Yes that shift rod connector screw is a little tight to get at, a magnetized screwdriver is a must if you're doing it without pulling the lower carb. BTW there's usually a drain hose running from the intake silencer back down to the crankcase, and sometimes a pressure hose from the motor to the fuel pump down under the bottom carb. This is the time to replace those, unless they're in really good shape! Either one can cause issues later, and they're often neglected since they're such a bugger to get at normally.
Your lower unit oil doesn't look milky, I think I'd listen to Rich and Gil and save the seal kit for later. Check the seal under the water pump carefully, wouldn't hurt to get the lower unit pressure checked before you bolt her back up?