Here are some suggestions/comments. I have done what you are describing, though it was not with AP cages or PVC cages. I don't have that setup anymore, so no pics unfortunately.
1) The closed cell PVC material that AP cages are made from cuts rather easily with a good hole saw. By "good" I mean new or sharp. The plastic has a thin solid sheet on each side, with foam in the middle.
Once you break thru the thin solid coating, the foam will cut like butter. Before breaking thru the bottom solid plastic, I would stop drilling and then drill from the inside up to complete the hole, or else hold a piece of plywood against the cage ceiling and continue drilling. You will be able to make a cleaner hole.
You may also use a jigsaw, but a hole saw will make a more uniform hole.
2) Before cutting or purchasing a hole saw, make sure to buy the desired diameter PVC pipe. It is a pain to try and enlarge an existing hole. Know your hole size before you drill. Carefully measure the outer dia of the PVC pipe and select the hole saw that is closest. You can either use a slightly smaller hole saw, then enlarge the hole via sanding, or you can use a slightly larger hole saw and fill any gap with epoxy putty. Please test first with a piece of thin scrap plywood to know what will happen.
3) Lucky for you, AP cages are made from PVC, as are the pipe fittings. You can glue a PVC bushing to the bottom cage inside ceiling. The piece of pipe will just fit inside the bushing and protrude up into the top cage and hold very well. No need to glue the pipe into the bushing. I would then press fit another bushing in the top cage where the pipe sticks up. That is how I did mine anyway - you do not need to.
An alternative to PVC glue is to use epoxy putty (sold at any DIY store in the adhesive section) to adhere the bushings. Epoxy putty can be removed if needed, yet it is very strong. And it will seal any gaps. You can also paint it to match your cage once it is cured.
If you want to be able to remove the top cage when needed, then don't use glue or epoxy putty in the top cage to seal the bushing or pipe in. If you want the cages to remain as a unit, then definitely use epoxy putty to seal the top cage bushing or pipe.
Also, you may want to stick the cages together. Velcro can work but leaves a 1/8 inch or larger gap, so make sure to leave some pipe clearance for that. You could glue them, though that is permanent.
