How do I force glue into a hard to reach hollow?
A syringe IS the best tool for such a job. Just make sure it has a nozzle/needle suitable to the adhesive used. They come in many different sizes. For large sizes you may want to locate veterinary supplies. Perhaps even talk to the local vet, who may be prepared to sell you a couple.

As for the PVA, it is generally not a good choice for tiles, especially if the tiles are in a wet area, although I can't think of anything more suitable for squeezing into such a small opening.