- specify a LAN IP for your ingress controller so it doesn't change.
- Use ddwrt/dnsmasq to point *.k8s.myhomenetwork.local to said IP
Once that's configured, you just configure the ingress hostname on services as you would "normally".
> This document specifies that the DNS top-level domain ".local." is a special domain with special semantics, namely that any fully qualified name ending in ".local." is link-local, and names within this domain are meaningful only on the link where they originate. This is analogous to IPv4 addresses in the 169.254/16 prefix or IPv6 addresses in the FE80::/10 prefix, which are link-local and meaningful only on the link where they originate.
Microsoft used to recommend .local TLD for AD deployment as a best practice, and nowadays there are companies stuck with this decision. Do not make the same mistake; unlike companies, you probably want your zeroconf stuff to work.
How it will behave will depend on your specific stack. Zeroconf aware (Macs, iOS devices, Linux with Avahi - i.e. most modern distributions) one will use multicast, zeroconf unaware (Windows) will use your DNS resolver. Devices (printers, etc) are a toss of a coin.