I don't believe, based on what you've posted, that you'll require use of either of the routing management protocols, nor should you require the bridge loop management protocol. The clients will reach this farm via its single outward facing carp(4) address. Your relayd(8) load balancer will manage the traffic to the back ends at Layer 3 and/or Layer 7, and carp(4) will manage back end redundant links as well.
I've set up a similar infrastructure with relayd, where the web servers were on separate platforms from the application servers and the database servers. I used relayd to manage all of the traffic between the web (nginx) and application (php-fhm) servers. However, all of that was in a lab environment; the infrastructure was never launched in production.
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