Sorry if I'm stating the obvious, but as you are "still new to Morgan ownership" has anyone advised you to tuck the rubbers under the hood flaps once the door's shut? Mine are pretty curly but that seems to make for a better fit and hence, rain exclusion.
Again, apologies if this is egg-sucking.
When the hood is up I usually shut the door for

holding the flap up. For myself I open the windows and reaching out through the windows with one hand holding the flap up whilst shutting the door with the other hand. For some reason

has problems doing this and if left to her own device pushes the flap out over the top of the sidescreen, which I don't really like.
If you have the easy-up hood you would do well to follow Dave's advice and stick neoprene pads on top of the windscreen pillars.
I fitted the new rubbers on the windscreen pillars but I did have to adjust the sidescreen position on one side. My recommendation would be to not remove the old flat rubbers as it will undoubtedly pull the paint off the pillars. When I looked at it I realised that fitting the new rubbers over the top of the old rubbers brought the outer surface of the rubber in line with the outer surface of the windscreen pillar, making a much better fit with no step. I did have to bend the sidescreen mounts a fraction to line it all ap well, particularly the rear mount to bring the top rear part of the screen in nearer to the hood. Cut the new rubbers where the front lower point where the step in the windscreen pillar and the material covered panel of the sidescreen starts to curve back. You can not force the new rubber to successfully curve back. I tried to do it and had to trim the rubber quite a bit as well as re-glue it a few times. I had not seen that the factory only fit it to the straight section.