MP2341 Maximum duty cycle

I’m using MP2341 to drive a load that needs 6V@850mA. I must use, as input source, two serially connected Liion cells and keep the current constant at least untill the Cells are dwn to 7.0V from their nominal voltage of 7.4V. But I see that I need min 7.5V as input to get the output I need. I simply don’t have enough head room it seems. I measure also 82% duty cycle maximum.
My questions are these:
1.Is there anything to be done with MP2342 to improve the situation?
2. What about using MP2410 instead? It has a specified duty cycle of typically 94% (unlike MP2341 which lacks maximum duty cycle in the data sheet). Will it work with less head room than MP2341?
Ramin Fardi