Pitch the " all in one" stuff and get some real primer.
Prime it first , then paint with "normal" paint. Go to a real paint store

there is no such unicorn as primer and paint in one, though they try and sell it. even on the back of its own label says for use over primed surfaces only.
Primer is glue in its simplest definition, thats why its primer used to make the adhesive bond between layers.
over the blue you should have any primer tinted light grey,I agree with christophern, but will add behr,valspar,walmart brand are not quality paints. If you had went to sherwin williams, told them what you were doing, you would have gotten what you needed, and well honestly, probably would be done already

I agree with otis AND also would say that any aged coat of paint that is clean, dull & dry could be considered as near-equal to a primed coat. But since no real weathering takes place inside and you have a fresh coat to deal with the rules change.
Usually compatible latex products will "knit" together when applied soon after as in a 2 coat system. I would be somewhat comfortable just applying a good quality finish coat over what you've done with the idea to do an adhesion test at some point.
Adhesion test: place masking tape [not painters blue] on the finish product a rip it off quickly. Does it pull the top coat off?