I agree there are lots of factors that come into play with a reblooming plant. I think any or all of the things covered in your post could affect it. But I would still guess there is a genetic component to plants that reliably bloom for a lot of people rather than just sporadic expression of the trait
Let me take another crack at this and come from a different angle.
There are perennial plant species that cannot rebloom in the same growing season. Usually that means that there is something required for those species to flower that simply does not repeat in the same growing season. So some species must experience a certain period of cold before they can flower. Other species must experience a certain length of night or darkness before they can flower.
Some perennial species can rebloom in the same growing season because they have no particularly special requirements or signals that they must experience to flower. Daylilies are one of those species. They do not need to experience a cold period to flower nor do they need to experience a certain length of night to flower. They will flower once they get to a certain size and then they will repeatedly flower when they produce the necessary increase in growth. In that manner they are like the more tropical perennials - tomato plants and petunias.
In a plant species that can only flower once it has experienced a cold period there is likely to be one or more specific genes that when mutated cause that plant to no longer need to experience a cold period to flower. The mutant plants will flower whenever they reach the appropriate size and then rebloom when they grow the necessary increment in size.
In a plant species that can only flower after it has experienced a certain length of night or darkness there is likely to be one or more specific genes that when mutated cause that plant to no longer need to experience that period of darkness. The mutant plants will flower whenever they reach the appropriate size and then rebloom when they grow the necessary increment.
In both those types of species, once reblooming varieties have appeared, we can reasonably write about genes for reblooming. Those would be the genes that need to be changed to allow the plant to be able to rebloom in the same growing season. That is not the case for daylilies as they do not need to experience any special signals to be able to flower.
That does not mean that there are no genetic differences between daylilies that affect their ability to rebloom. All the factors that affect how a daylily grows and flowers are likely to affect their rebloom and may be genetically different between individuals. As an example, we might have two daylilies that are otherwise physically alike but one has ten buds and the other has 30 buds. The difference in bud count will be based on genetic differences. It is likely that the ten bud plant will rebloom more often and more reliably than the 30 bud plant given the same growing conditions. I would suggest that although the two plants rebloom differently and are genetically different that they are not genetically different for rebloom but more simply genetically different for all the aspects of growth that affect flowering.
Equally a grower will find it easier to have the 10 bud plant rebloom with poorer growing conditions than to have the 30 bud plant rebloom. The genes involved would be those that determine the difference between 10 buds and 30 buds rather than genes involved specifically in rebloom.
As you mentioned, there are a lot of factors that come into play; those factors will be at least partially genetically based and genetically variable between individuals. What I am suggesting is that none of those factors are specific to rebloom - they are common to growth and flowering in general. Once special requirements for the ability to flower at all are removed, flowering and reblooming become characteristics that are dependent on general aspects of growth and those are affected by many factors which themselves are at least partially genetically based and may differ between individuals.