I'm not the worlds best climber (my power to weight isn't that good due to weighing a healthy 90kg (6'3" tall) but I have got better and now except that only a diet / lifestyle changes that I don't want to make will make me much faster.
A few tips (that work for me):
Change into granny at the beginning of the climb or on a flattish section. Dropping into it when up a steeper section is not good for your transmission and will lose your momentum.
A road bike will help you learn to 'love' hills but it's not the same as offroad. On road it's far easier to get into a rythym as the gradient is more constant and often gentler. Off road you need to react to the terrain which may mean some high intsity burts (where recovery due to fitness comes in).
Don't do a someone up there ^ said and look a few metres in front of you. Especially on technical climbs you need to plot your route through obstical as you would if descending. looking ahead also stops you front wheel lifting and wandering. Chunk the hill into sections challanging yourself to get to the end of each one and then the next. it's amazing how quickly the climb can be over when tricking you brain this way. If you want to get faster then focus on a flatter or easier section at the end of a 'chunk' and power up to it then use the easy section to recover.
Always ride over the top instead of stopping - for me I recover quicker and can control my breathing better that way.
I actually find climbing rigid singlespeed easier than by full suss but the standing up stomping on pedals doesn't work on a fullsuss and is had to sustain on longer rides. So for me SS is not necessarily good climbing training.
Train on your own sometimes - riding with others who have different weights and fitness can be demotivating and sitops you finding your own climbing pace.
Finally make lots of excuses about weighing 3 bikes worth more that the whippets you ride with
Hope that helps.