I believe (could be wrong) that the slots applied for the summer season were to come out of BA's portfolio, former Flybe slots held for domestic routes until recently. Just because Eastern weren't awarded any of their own doesn't mean it won't happen. As it turns out if it was to start it's probably not going to be on 6th July as that would be far too soon.
Oddly there's still been no mention of the Southampton route starting which is still bookable as I post this.
Good news on Amsterdam returning, even though we all knew it was bookable from 3rd August anyway.