Estimating yeast cell counts in this fashion is inexact, but probably close enough to get the job done.
Yes, you will likely be overpitching if you use the entire yeast cake. Yes, you can just go ahead and put your fresh wort on top of the yeast cake. You can make perfectly good beer this way and be happy with it. You may also get off-flavors or unexpected flavors from the overpitch. Some people say more esters.
An easy way to deal with this would be to pour the yeast cake out into one or more sanitzed jars/containers and use the amount you think is appropriate. 1/3 is probably what you need. 1/2 if you want to be conservative.
This also would give you the benefit of using a clean fermenter that doesn't have all the mess of the previous fermentation.
I've used whole yeast cakes in the fashion you plan to do with good results. The process of pouring out and using only a portion is so simple and effective that I haven't done the whole yeast cake thing in years.