If you're using down files to determine startup order, do you have a different filename (LittKit calls it 'reallydown") to take over the former functionality of the down file (to make the service down for awhile, through reboots)?
There's no need for such a thing when your services are managed via s6-rc. The machine state you want is encoded in your service database, and your stage 2 init runs s6-rc with the correct arguments to bring the machine state to the one you want. Through reboots, the same state is enforced as long as the default service database doesn't change.
I really recommend that you read the s6-rc documentation if you want to understand how it works. -- Laurent