Hi Rob,
The short answer is yes, but most likely not the way you started :)
I'm currently interviewing organisations on how they used impact maps for a new book, and there is a pattern emerging around restructuring the scope of a project -- where the scope is known (or they think they know it) upfront, but there is a lot of work, potentially dependencies, so alignment on the sequence of work is important, and ensuring that people keep the eyes on the prize.
in this case, the actors aren't the individual teams... they might fit around deliverables, but it's not their behaviour you are likely trying to impact. if the goal in the middle is to reduce operational costs, then by migrating some service and associated set of features, you may help someone (eg an inventory manager) perform their tasks (eg generate inventory reports) cheaper. breaking things up like that might help you figure out which parts of the infrastructure aren't needed any more, which are just not that important, and which would be low risk to start first (= those impacting low risk activities) or which would be high reward to do first (= those with a high operational cost). in addition, this may help you build up vertical slices of your infrastructure that's moving, and reduce business disruption. for example, you might discover that for a particular activity, you don't need to migrate the whole database but only a few tables, or certain columns in certain tables. then for another activity you may need to migrate additional tables etc.
not sure if this maps to your case or not, but if it does, that's the approach I'd try.