Well you are kind of right and kind of wrong. First of all though 6 90s in a system is a lot! Is there some way you can either put in some 45s in place of the 90s or even use flexible hose to get rid of some of the 90s.
Now onto the calculation parts. According to the charts I have seen, they are equating each 10 foot section of pipe to an equivalent feet of head due to friction loss. Then they equate each 90 degree fitting to a number of feet of straight pipe, not feet of head.
So in your case lets say you have 10 feet of 1" pipe, then you have 6 90s, each 90 is equvalent to 2.25 feet of straight pipe, so that is 13.5 feet of pipe. Add these together and the total piping in your system is 23.5 feet of pipe. The total feet of head loss for this is about 6 feet. Add this to the four feet of head you said you already have and you have 10 feet of head pressure for your pump. Look at the pump curve to see what your flow would be for the pump at that amount of pressure.
Me personally I think this is WAY too much thinking and doing your guzintos. I say look about what size pump you need, maybe buy a little bigger one and use a valve on the outlet to slow it down to the flow you need.