Nice, we evaluated their Seed product but didn't pull the trigger, which caused me to eventually roll our own. I'm pretty proud of what we ended up with but due to reasons we ended up with _hundreds_ of lambdas, for which a full re-build re-deploy took around 45m (Go lambdas).
We used Go and the Serverless framework (ugh), and if I had to do it all over I would probably just use AWS SDK since it would make doing the "diff" to redeploy dead simple, since everything is just a binary to build.
Your use case definitely makes sense for Lambda APIs though! I think my complaint is more directed at APIs that back frontends. We had a JVM lambda API there for a while that was horrificly slow startup unless you set provisioned concurrency, which gets expensive fast.