I can't say anything about promising. The hard part seems to be building an apparatus that works, and I don't know how to do that. I hear of short-lived superpositions with increasing amus or daltons but I can't deal with those units without the newest SI prefixes (fun facts, 666 Yamu is a bit more than 1 kg; and there is maybe about 0.666 YMsun locked up in observable galaxy clusters).

HN user ISL <https://news.ycombinator.com/user?id=ISL> is probably au fait with recent quantum gravimetry experiments.

The Müller group at UC Berkeley came to my mind. They did a recent paper <https://arxiv.org/abs/2210.07289>.

Gavin Morley's group at Warwick University is doing work in the area <https://warwick.ac.uk/fac/sci/physics/staff/academic/gmorley...>. He has what looks like a useful bibliography on the subject too: <https://warwick.ac.uk/fac/sci/physics/staff/academic/gmorley...>.

Finally, while not really related to your question (except that greater-precision gravimetry is likely to mean smaller superposed masses are useful), https://www.nature.com/articles/s41586-021-04315-3 is extremely cool, and I wish it could be sent back into the heyday of https://en.wikipedia.org/wiki/Time_Team . (ETA: Müller's group, similarly, https://arxiv.org/abs/1904.09084 .)