Regarding your top drawing, if that middle splitter is a 3-way, your middle TV gets a 50% signal, the adjacent TVs get a 12% signal and the two outer TVs get a 6% signal. You want to split the 722 signal two ways and feed two more splitters and feed TVs from those splitters. Those four will then get a 25% signal each and may be OK. You can then try splitting one of the TVs to feed a fifth or then use the 3-way. If you are using a 3-way splitter, one tap is 50% and two others are 25% signal level. Those last two splitters cut the already weak the signal in half and are not needed.
That would work. Keep in mind it seems there may be an underlying problem & an amp may not help. Too many splitters, bad connectors and so forth. The only way an amp would be of any benefit is if you had all home runs back to the amp location. If you try to ampilfy a distorted signal to begin with, you still end up with the same result, noise.
I used to have 7 TVs and at least feed off of 2 dish boxes. I had a powered 4 way splitter and one of the feeds from that one fed another 4 way splitter. Essentially a splitter in the attic for the 2nd floor and one in the basement for the first floor.
Just be aware that you can over amplify too. In my set up I had 2 feeds coming in at about 75 feet to the first splitter. All the rooms off of this one were within 50 feet. Then one output went 75 feet to the second splitter and all runs were less than 50 feet. All in all it was quite a distance of cable but it worked fine.