Hello @Lee Brown - Thanks for reaching out!
I can't speak to the cost-effectiveness part since there are many factors to take into consideration to be sure that one option is going to be less expensive than the other, or vice-versa. In order to use APIM in front of your VMs and round-robin the calls to them, they'll need to have their own, unique URLs so they can be added as different backends -- can that be the case with your current setup?
If you're going to be needing other load-balancing features beyond round-robin-ing, it's probably best to stick with Application Gateway: Choosing a gateway technology
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