The filter and line routing may be causing enough restriction to give you the fuel-starving problems you are having (pic 10). The line is bending quite a bit from the petcock to the filter. There isn't much room there, so adding a filter can cause more problems than it solves.
Easy enough to just run a new line without the filter and give it a try. If that works, I'd be sure to use the factory inline filter.
If that doesn't change anything, I'd pop the gas cap when it starts to run poorly (listening for air rushing in) and see if that corrects it.
That intake boot doesn't look too good (pic 4), I'd find a replacement.
The vacuum line to the petcock is also a possibility.
Check inside the tank for the condition of the screens on the petcock. Try switching to Reserve when the problems start to see if that changes anything.
Either way, it sounds like a fuel flow issue to me.
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