Why not experiment with multiple variations. For example, as part of the experiment, run own DNS, use non-standard DNS encryption like CurveDNS, or even no DNS at all, use non-standard port for HTTPS, self-signed CA, TLS with no SNI extension, or even TCPCurve instead of CAs and TLS. If non-discoverability is the goal, there are inifinite ways to deviate from web developer norms.
If "the internet fails to find the subdomain" when using non-standard practices and conventions then perhaps "following the internet's recommendations", e.g., use Cloudflare, etc., might be partially at cause for discoverability.
Would be surprised if Expanse scans more than a relatively small selection of common ports.