Holy cow are you lot still going?
Question is should I be upping the HR to 85-90% when I’m doing these or should I stick to the zone I’m going to be climbing the big mountains at in the summer?
Don’t use the HRM to stick to the guideline numbers, they can be way way out. The zone in which you should do long climbs depends on a whole load of factors, your heart just responds to those factors, it doesn’t dictate them. So if you want to know what your max sustainable HR is do a long climb and then see what readings you get.
To be honest, on really long climbs you should automatically tend to your max sustainable anyway by definition, so you don’t really need a HRM for that. The HRM is useful if you want to train at that zone without actually having to do a really long climb.
So do a few long ones, see what the HR settles down to, and then that’s the target you want to ride either over or under depending on your training goals. To increase that pace, I think maybe you want to work on aerobic power, perhaps with intervals – but not sure, do some googling.