April 21 ???
And no eggs....even from a laying workers???
I would not be releasing any queen after 3 or 4 days without doing a finger test as a minimum.
Finger test.....After 3-4 days, pick up the queen cage. Cage you lightly shake or move the bees off the cage with your finger? Or do they have death grip and will not budge?
6 weeks....or 42 days is a long time with no queen, and yet no laying worker. You may be missing something..... An unmated queen, a queen unable to lay, or something else. I have seen hives linger for months while being loyal to a queen that never layed an egg.
And that old "shaking out laying workers" is the biggest piece of urban myth baloney you will ever hear. I shook many laying worker colonies.....and it does not work. If you have laying workers, then combine with a queenright colony.
Keep us posted how this works out.