I always allowed the babies to nurse until they were weaning age 10 weeks before I would try to milk any of my goats.
The doe will produce according to demand, the babies suckling all of the time creates a demand and the doe increases production to meet the ever increasing demand.
As for the makeshift vacuum not sure I would advise that myself. But then again I made a breast pump for my wife 26 years ago so I probably have no room to talk.
As for the milking you mentioned not working the udder, you want to work the udder and work the milk down and you also want to take your time, it takes a little bit for the milk to work down sometimes. I found that first year milkers generally did not produce all that well and I never had any Nigerian dwarfs that ever produced much at any age.
Most of my herd was large Saanen mixes cross bred to Alpine, La mancha and Nubians. The large goats could produce up to 1 1/2 gallons a day each but my Nigerians and Nigerian crosses generally maxed out at about 1 quart a day being milked twice a day. As the Nigerian blood became ever diminished down to about 1/4 Nigerian and 3/4 full size the milk production went up to match that of the full sized goats.
As for milking the Nigerians, I had a heck of a time with that, I have large hands and couldn't hardly pull it off with those tiny little teats. Luckily I had my wife and six kids who ranged in age from age 2 up to milk the Nigerians. The other issue with the Nigerians is that they commonly sat down while we were trying to milk them, I literally had to hold many of them up while they were milked to keep the udder out of the
bucket. The other challenge was that they are so short it was tough to even fit a bucket under them and even on the milk stand the wife had double over in her wheel chair to get under there.
How much milk are you looking to get a day?