There’s two ways around the symptoms you’re trying to treat:

1. Don’t bother with internal vs external. Always route through external which gets encrypted by the origin cert to CloudFlare and then CloudFlare to your browser. This is simplest in that you don’t need to manage two sets of DNS records and you don’t end up with different certificates for the same domain (in the odd event where you end up needing to do something like certificate pinning). Or;
2. Just add the origin cert to your systems’ trust store. You know the certificate, it will encrypt the traffic anyway, also you’re accessing the service via intranet so there’s really no attack vector here.

Probably worth calling out that although 1 feels like there’s more hops (and there absolutely are), with any decent internet, you’re probably not going to feel it. This is because the edge server is probably situated very close to your ISP (that’s how they make sure everything responds quickly) so your over all round trip should only be affected by a negligible amount of time that you most likely won’t notice.