I realize this is not the answer you are looking for, but i think it´s a point that needs to be made.
While it is possible to induce consecutive spawnings, doing so for selfish reasons is objectionable. The breeding season is determined by hormonal changes. Those hormonal circumstances are only possible given certain environmental conditions, but also, physiological ones (both are essential, one without the other won´t work). It takes a lot of energy and resources. It takes a heavy toll and not just on fat reserves.
Given that domestic axolotls tend to breed easily and do so in consecutive waves, even if environmental conditions are not "perfect" (and this is the important point, because they are not restricted to breeding in a specific season), it seems to me that if your animals have stopped reproducing, it may well be a matter of physiology. In other words, they may have stopped breeding because continuing to do so is not physiologically "wise".
Captive conditions usually allow them to produce very large spawnings and for longer periods than would otherwise be normal, as well as at almost any time of the year, simply because resources are abundant and constant. There is a limit, though, and hormonal chains will regulate themselves to become inhibited when that limit (either physiological or environmental) is achieved.
Inducing more spawnings could result in problems, like the depletion of certain reserves, leading to metabolic disorders, shortened lifespans, etc...
In short, if they could afford to reproduce, they would do so, as long as environmental conditions are not too restrictive, which is unlikely for domestic axolotls in normal housing conditions. If they aren´t, and you force more spawnings, it will have consequences, and since i´m sure you love your animals and want the best for them, you should be able to sacrifice your desire for entertainment in favor of the health and well-being of your animals.
