What's an alternative to shoe moldings?
Quarter round and shoe molding are two different things. 

Quarter round is just that...one quarter of a circle. Shoe molding, on the other hand, is much flatter with a rounded top. 

Lots of people install quarter round when they intended to install shoe molding instead. 

Choose shoe molding over quarter round whenever possible, as it looks better. 

As for your question, it sounds like your baseboard and shoe molding is 'floating' above the floor. The best solution would be to simply remove the baseboard and molding and put up new stuff (or if the original stuff is of a particularly good finish/quality, then out it back)

If you don't want to remove the baseboard itself, you could remove the quarter round and then look for trim pieces that can act like a shoe molding but a bit taller so that they cover the gap. Visit your local big-box hardware store and you'll find an entire aisle of molding styles to choose from.

If the gap is especially large, you may want to use a molding to cover the gap, then a shoe molding at the bottom of that to create a built-up baseboard.