It sounds as if you did a lot of things right in the package installation…but from my experience with shaking packages it sounds as if there was a queen-related problem within the hive that caused the bees to vacate. The assumed queen problem could be due to a few factors:
An injured queen or a queen physically distanced from the workforce bees…I’ve seen them drop off a frame and crawl to a corner on the bottom board and left unattended by the workforce. It sounds as if you may have placed the package inside the broodbox hoping that the workforce would crawl out of their screened shipping box and not physically shook the worker bees on to the frames?
A queen that wasn’t accepted by the workers…because a) the queen hadn’t been with the workforce bees for at least four days before being released b) There was a virgin queen in with the workforce bees
Method of queen release…did you pop out the cork on the queen cage, put a nail hole in the candy plug, or did you tear off the screen and shake her into the brood box? Packages I used to get from California (3 day trip) had the queens left in their cages and placed cross-wise on the frame top bars and left for a day or two - then released…New Zealand packages (4 plus day trip) I could direct release by tearing off the screen of the queen cage and carefully let her crawl onto the frames.
Caged queens…when released… are notorious for flying off into the sky…never to be seen again…when I direct release queens it is always done under that plastic sheet. I use that plastic sheet under the Flowhive lid to seal in heat and moisture needed in my climate to rear maximum brood.
If the bees are placed on new frames, I try to provide accessible resources for them…i.e. syrup and pollen patties…note the small stick placed crossways near the syrup frame feeder providing that ease of access…even when there is forage around them to gather because you never know if you are going to get a week of cooler weather. The feeder is inside the hive where the syrup warms to the temperature of the adjacent cluster…and I never do an inspection for 3 weeks when I see that fresh wax being built under the plastic…all is well. But if I don’t see that fresh wax under the plastic sheet within several days of package installation, something is amiss.
When it comes to deciding how to initially start your first hive, as you know, your choices are either nucleus colonies or packages. The nucleus colony should have an established queen and built-out frames to help anchor the colony. The package bee scenario doesn’t have that anchor…but it doesn’t have the pending threat of disease (chalkbrood, AFB, nosema) or parasite loads inherent in used equipment/brood… this has been our experience.
I know it’s an expensive loss…and tough on your optimism…but it seems everything I’ve learned about beekeeping has cost me both…don’t give up!