I have thought about the right way to do local DNS for my home network, one that works without a lot of trouble on different desktop OS, tablets, game consoles, etc.

I am afraid that one day web browsers won't let you visit something like

   http://10.6.28.128/

which is the kind of URL I visit to see the "control console" for my smart home and other services on my home server.

I'm going to get flamed for this... but why would you need TLS/https on services that are ONLY accessible from inside your home network? If you have bad actors on your network, you've got bigger problems than un-secure websites.

Anyhoo, if you must, then roll your own CA, get it to generate certs, put the CAs root certs on your clients, and you should be good to go. This route also means you can have something like .myhouse as your TLD if you so wished.