What tools exist to measure work meaningfulness?
There are a bunch of them! For a great review of many definitions and measures of meaningfulness, see if you can get a copy of A Narrative Evidence Synthesis of Meaningful Work: Progress and Research Agenda. The authors are pretty responsive in my experience and will send you a copy.

One thing to keep in mind, though, is that there are a bunch of different definitions of work meaningfulness. Everybody has their own approach, some are better than others (i.e., more likely to actually measure meaningfulness and not something related like engagement or intrinsic motivation), and there isn't really a consensus yet. The WAMI you mentioned is built by highly-regarded meaningfulness researchers, is very commonly used in studies of meaningfulness, and I think it's a great "safe bet" measure for getting overall work meaningfulness.

However, if you're looking to zoom-in a little and look at sources of meaning (is it the challenge of your work that you find meaningful, or bonding with coworkers?) like those described in On the meaning of work: A theoretical integration and review, then you might want to check out the Comprehensive Meaningful Work Scale.

Hope that helps!