My advice is to concentrate on keeping the pups growing. The original plant (let's call it mom), has bloomed and made pups. Mom is on her way out because the plant only blooms once, then dies. That is not uncommon in the plant world. As the pups grow, the outer leaves on the mom plant die. This is because the plant uses the meristem to bloom. The meristem is the only place a Brom grows from, and once the meristem is used to make a flower, it is used up. Same thing happens on bananas and other plants. At any rate, as the outer leaves die, you can easily detach them. No need to repot for years if you keep the cups damp enough and add a dilute fertilizer from time to time. Many Bromeliads do fine with little dirt. Guzmanias mostly use their roots for staying upright, much of their nutrients are absorbed by their trichomes.

The goo is normal for a number of Guzmania species, I would not worry. AFAIK, all Guzmanias would normaly pup before expiring, but I have had them die on me without doing so. They can be hard to keep alive, especially if grown in a greenhouse and then moved to dryer conditions. As for them having a blooming season, that's news to me! I am sure that you can have blooms year-round, depending on the species or hybrid. They need little or no fertilizer.

I would plant them pot and all. It's just easier.Here's some inspiration for you. Then click where it says landscapes for more eye candy. Here is a link that might be useful: Guzmania

There is a Bromeliad Forum where you might get more responses. Here is a link that might be useful: Bromeliad Forum