Thank you all for weighing in, I really appreciate that.
I think I might try putting the plant on another room's windowsill, where there's no heating turned on during winter. It's not much of a temperature difference, but it might just do it.
The posters ahead of me are much more experienced so I would take their advice on things. I just wanted to let you know that I live in NY and about 5 miles from NJ so our climates are similar. I rebloomed my first cymbidium this year. It spent most of the summer outside on my patio which has trees overhead. It's best sunshine was in the early morning. I let it stay out until the temps were pretty cool at night (40s/50s) but brought it in before it was freezing. It bloomed beautifully on two spikes in October and into November.
Now it is wintering inside in a South facing window at about 55 degrees night and into low 60s during the day (a guest space that the heat is only used when company comes).
I keep it evenly moist, but never let it sit in water. In the spring I will give it some Osmocote and it will probably get fertilizer when I fertilize the other orchids as well before it goes outside again.
Yeah - a while ago, someone suggested me to put cyms in the fridge overnight to bloom. I thought it was crazy and never tried! But, who knows? Another option is to buy one of those indoor greenhouses.