2nd base might be a home run

[David]

Dot, one idea that comes to mind is if you have a baseboard which has some flat surface area in the first 2″ near the floor, you could add a strip of doorstop (in colonial, modern, etc. to match your existing style), then put down your base shoe/quarter-round. This will give you an extra 1/2″ of coverage, and bridge the gap.