This is tricky for a couple of reasons. Adding a person as a co-author of a paper requires, at least, their agreement. Normally it also requires actual contribution to the work, but that idea is compromised in some fields, such as when a PI only contributes funds that make the research possible. Second, even giving an acknowledgement to a person normally requires their permission. This is more important in some fields than others. But if you attribute controversial statements to another you need their permission, generally.
However, there is nothing especially wrong about pushing someone a bit to elicit their permission or participation. This is especially true if you don't have a power (superior-inferior) relationship with them. Forcing subordinates is often done, though usually wrong. But that doesn't seem to be the relationship here.
I would send them each a note that you would like to pursue the topic and publish some results when done. Offer them co-authorship if they will participate effectively, but only acknowledgement of past contributions otherwise. Suggest that they talk it over with their own advisors. Then evaluate what you hear back.
I'm assuming above that all results so far are preliminary and tentative.
If there is nothing to do but the writing or minor clean-up this would be a different situation. In that case, write it up with all of you as co-authors and send it to them for approval or updating. Yes, you would be doing a large part of the work yourself, but that might be worth the effort.
The tricky thing here is that I don't know how much contribution each has made so far. Perhaps they are already due co-authorship of anything you produce. You will need to deal with that collectively.
If they have already contributed substantially, then a joint publication seems warranted (three co-authors). For that, all you need to do is get their permission. If they are unable to help work on the paper (no time, advisor objects, ...) then this might be your best option. Even a generous interpretation of substantially might be warranted.
I assume that, unless the topic is controversial, a publication is more valuable to them than to you, who already have a position.