The only two methods used for poropagation is by seed or division.
A "hybrid" is a cross between to plants & when they flower & set seed there will be about 47% of 1 parent 47% of the others that leaves 6 % which could be of any combination.....
Comercial growers use the 2 parents & take precautions to insure the parents do not self polinate and/or another unknown plant does not polinate either parents..

Bummer. Is it possible to keep the plant alive indefinitely through division? Or is it doomed to fade away just like the whole plant would? It sounds like I am out of luck as I only have one plant and in any case there is no practical way to prevent external pollination.

Columbines are perineal and will return each year larger and more vigorous than the year before. If you give it 2-3 years to become a large clump and then divide it, you will always be sure to have that particular plant. You might save some of the seeds and see what comes out of them. I never saw an ugly columbine, so what have you got to lose? Cheryl