You'll find it extremely difficult to clean the spring via the small screw hole, BUT Edison DD & Amberola grease seldom solidifies unless it's been exposed to extreme heat, unlike the graphite grease that Victor/HMV & other companies used. It does dry out a little, but nowhere near as much as any of the others I've come across.
Before pulling the spring out for a proper clean, I would try adding 2-3 teaspoons of vasoline to the spring barrel & existing grease (which is apparently vasoline & graphite flakes).
That should be enough to mix with the original lube & return it back to it's original consistancy (or pretty close to it).
I've only done this once (feeling lazy
) about 8 or 9 years ago, and I haven't heard it bump once since, although it's not a machine I use more than a few times a year.
To be honest I cant remember what I used on that one to get the grease/vaso in the barrel, but I have since topped up a few of my other Edisons, by using a large syringe that comes with cartridge refill ink that I buy. I just pull out the plunger, load it with vasoline, replace the plunger and inject it in the hole with the spring fully wound. Then I let it run down (after replacing the screw) & rewind it a couple times to mix everything together and spread it evenly over the spring.
I'd certainly give this a try first, and if you find the original lube is too far gone & the spring still bumps, all you've lost is a little bit of vasoline.