I don't say that to be glib, I say it because I suspect it is actually the cheapest path to what you want.
It might make sense to hire someone to come and take the bike and change the tubes every year or something like that. Or perhaps hire them to deliver a new bike once a year, and take the old one away (depending on how much easy money they smell when you ask them about this, they might even give you some of the proceeds from selling the lightly used old bike).
What do you guys do to your bikes?
The biggest maintenance I've ever had to do on my 10yr old bike was putting on new tires and brake shoes. Any bike shop will change those for you and give you a full check up for like $30 (materials included).
Unless you leave your bike outside in the rain all the time it should last pretty much forever, needing little more than some air, oil, and re-fastening of the odd screw.
I don't think either of my suggestions are particularly sensible (unless maybe you are in a situation to have your butler take care of it), but they are possible, which compares favorably to the idea of a maintenance free bike.
Solid tires are available, but the reason you rarely see them is that they ride like bricks.