How to keep a small Li-Ion battery on float for backup service?
You can float them at any voltage above the minimum if you want to. Just get past the idea that you need to maximise capacity, and have fastest possible recovery times. You don't.

I have floated them at 3.7V, which means that I have a very loose +/-5% tolerance and still guaranteed to stay below 3.9V (which is roughly what the cell settles at when left alone for a good long while). 

So you can use almost any regulator to float them. LM317's, TLV431's , even using a zener is possible.

You just have to work out the tolerances over temperature (includeding the battery tempco, and what you want the worst case max voltage to be and design accordingly.