here's my 2p's worth
As with most cycling games going uphill is about stacking the odds in your favour in the first place and making things easy for yourself.
First of all make sure your seat height is right and your getting the right amount of leg extension through the pedal stroke. This is crucial for efficent up hill pedalling
When your cycling up the hill make sure you go slow enough, spin steadily. Don't get caught racing or going at others pace, settle into the grind right from the start. Ideally you should be going at a pace that allows you to hold a conversation with the person next to you, this means your below your aerobic threashold and that the exercise is sustainable. REMEMBER YOU CANNOT GO TOO SLOWLY
When your spinning the pedals think in smooth steady circles. Dont spin out, if your spinning like a loon then change to a stiffer gear.
If your bike isn't low enough geared to allow you to steadily spin an easy gear then invest in a cassette with a wider spread. I use a 34-11 on my enduro and its brilliant. The bike is a big hefty fat tired beast but will grip on the ups like nothing else I've every ridden. Really low gearing allows me to cycle past the light n fiesty bikes and riders with a smile on my face.
So keep is steady and be determined not to stop, ensure you plan right from the start not to stop. Problem you've got is you've got into the habit of stopping, you need to break that habit. Instead of starting the new you on the Mam Tor climb think about an easier one that you can 'just' do without a pause and try taking it A LOT slower and steadier. Hopefully you'll find it easier. REMEMBER YOU CANNOT GO TOO SLOWLY. Work through a few challenge climbs and build on successes before tackling your nemisis.
Once you've unlocked the secret of riding the ups it will make a difference to your fitness and this can all catch you up in a spiral that will lead to significant improvements in your technique and fitness
Hope this helps
Ian