Hi @ndmetherall,
So long as the data meet the criteria needed for use in InVEST, where the data come from shouldn’t make a difference in how the model is running.
Using a UTM projection (looks like maybe zone 60s would be best for Fiji?) should work well except for Web Mercator. As for reprojecting itself, Stacie has a great post on another thread (How to deal with the error message "Dataset must be projected in linear units."? - #2 by swolny) that you might find useful as well.
Please let us know how this goes!
James