Here is the charger I was talking about. It's based on the Microchip MCP73833 charge management controller which is the same controller I use in my own mods. It's a very nice full featured controller, programmable to 1 Amp.
20C LiPos typcially have a 2C max charging rate. 1C is perfectly acceptable so for a single 1000mAh 20C lipo a 1A rate would be fine. Using two cells in parallel would split that rate in half so each cell would be charging at 1/2C. BTW, a 1C charging rate always works out to one hour. A 1/2C rate is always two hours. Though, charging is not 100% efficient and current drops down when the charger gets to constant voltage mode toward the end of the charge cycle so a 1C rate works out to around an hour and a half in reality. A 1/2C rate would be more like two and a half hours.
With respect to the fuse, I mean the F1 fuse shown in your schematic. I would relocate it in series with the number one LiPo cell so each cell has a fuse on it. A 20C 1000mAh LiPo can handle 2A input current continuously from the other cell so you can probably get away with something around a 3A trip since the cell only has to endure that current for the time it takes the fuse to trip. The trip current spec for a PTC fuse is misleading. They trip at any point above the hold current, it just takes longer.
You'll have to take a bit of an efficiency hit since PTC fuses with a lower trip current do not have particularly low resistance. You'll want to select the lowest resistance you can. You will also be limited in output by the fuses.
That's the advantage of using two charging boards. It allows you to avoid connecting the cells in parallel which simplifies things.