Only need to solve the web-based wallet part.
I think a great way to encourage people running nodes is by making it easy to connect a feature rich and network light mobile wallet to you own personal electrum-type server. That way your phone, tablet, or frequently disconnected because you drag it everywhere laptop can have an instantly available wallet without trusting third party servers.
The electrum server and stratum are freely available, but it would be nice if some of the bigger bitcoin news and information sites put together a guide for the mobile bitcoin user doing business in person.
This remote computing seems like a good idea. Mobile Phone stores private keys and connects only to home computer. Home computer handles blockchain, node, etc., but not wallet.