A 400x400 bed should be flat enough (if its any good, so might be worth skipping the autolevel routing if you can. If its not flat enough, you need a new bed that is, as autolevelling is a software attempt to fix a hardware problem, and just doesn't work.
Prittstick, hairspray, a 20% PVA/Water mix, whatever works. Though its most likely its not its adhesive abilities, but more its closing the gap between the bed and the first layer. I cannot stress enough that you need to get a good first layer.
The print I showed above shows that you should be able to get a small, thin, minimal bed contact, item to print without become detached with a good level bed. Worth experimenting. Also, a cube, for example, should have a very smooth finish on the bottom, not one that looks blotchy or stringy.