I resolved the issue – my VPC had a custom DHCP option set, which was adding the subdomain to the nameserver search list. This subdomain was the same one I set up as a wildcard DNS record for Okteto to operate under, so every DNS lookup was matching the wildcard DNS record, and thus resolving to the address of the load balancer.
Possible solutions are to remove the custom DHCP option set, or pick a different subnet for Okteto than the one assigned to the VPC as a whole. I went with the former, and the application now works correctly.