Why don't just consequently use $11_{2}$ and $11_{10}$ and teach it the same way it's done at universities? I don't see how this would be any more difficult than starting confusing things with symbols that just add complexity on top of a difficult thing.
The most confusing thing in school for me was when teachers tried to simplicate stuff ...
If it was me, I'd teach them the whole abstract thing and leave simplified constructs to the slower mindsunless your students really need it.