That sounds like an impossible task to me to be honest. Why not get rid of it and redesign the garden so that you have a hard surface/path that you can sweep, plus plants in beds that you can weed??

I've actually done just this Nannycats !!!
It was in a previous garden and once done it looked great, i was really pleased with it :-))

I think the first job is to remove those weeds/seedlings - by hand (hard work) or weedkiller, then i would push away sections of shingle, cut through the membrane (supposed to stop weeds etc from rooting) and plant 'into' those areas.

Keeping it free of debris is the same as in any garden - irritating and hard work !

I'd love to see what mine looks like now ( 15 years on!) !

I would rake up the shingle and see how much debri has gathered under the shingle? from what you say I suspect its quite a bit. If so the weeds will just come back? You need to remove the debri and relay or even replace the membrane then replace the shingle hose it down to clean it, then you can make cuts in the membrane and plant it up. The debri is best put in your green wheelie as it may be full of seeds.