A few thoughts:
Conjoint isn't typically used for pricing, but for finding the attributes of products that maximize consumer desire / utility
Conjoint is a hierarchical Bayesian method... so also Bayesian Optimization
I like the idea of a continuous optimization via API rather than a survey, tightens up the feedback loop for smaller SaaS products
You're going to want to get some academics to back your theoretical grounding - it's actually a sales thing if you're ever trying to sign larger contracts.
There is no such thing as a "fair" price, just the market price
How do you prevent users from feeling cheated when they realize someone else may get a different price? Or worse, just refreshing until they get the lowest price for the tier they want? This is probably the biggest sticking point of your service - larger companies probably can't get away with changing prices after launch.
Congrats on the launch!