the inline filter is there because the bike is missing a screen or two. Screens provided by the manufacturer allow the tiny stuff (stuff that clogs paper filters) to pass through..
If all screens are intact, the inline is there for no reason.. but whatever.. Flow from the tank is good at this time.
_When I let go of the throttle, the bike gradually slows (from 19mph), and at 10 mph the bike vibrates a good deal, and by 7 mph the engine cuts out_
...points to something capable of seriously restricting fuel supply or interfering with the carb's ability to provide the correct air:fuel mixture.
Does the choke open completely? Are choke and throttle cables adjusted correctly?
Various bikes have different means and methods of applying and releasing choke. I'm not familiar with the Pinto's.