I've recently been persuaded to stay cleated when going up every hill, and have learnt (I think!) how to uncleat and get off at the last moment if my energy runs out before the top. Learning how to sit down and spin smoothly (i.e. pulling up efficiently so I'm pedalling in circles), however slowly, has been like a light-switch coming on. I'm not speedy up hills, but I just don't want to have to get off and push, unless I have to.
The other matter, about the road junction at the start of the climb... If I don't feel I've the technical skill yet to handle such a junction, I get off and walk across it and start from the other side, a few yards beyond the junction so cars coming round the corner get a good sight of me and have time to take avoiding action if I'm wobbling. Am I a bit of a coward? Maybe, but it stops me having any anxiety.
I've got a couple of local hills that used to get me off the bike... but it now gives me pleasure to see how much easier they feel, thanks to increased fitness and better technique (plus changing to a 30t on the Ruby & 34t on the Genesis!) Good luck! x