Throttle lag is a symptom of lean condition, but 4 stroking under load is a symptom of rich condition, so maybe that back pressure will help to even things out.
As you are describing the symptoms of two completely opposite conditions, I think the problem has to be elsewhere than just the carburetor jetting.
If you only try fitting the cap, not fitting the cap and then keeping it on while jetting the carb, maybe you're not seeing a true picture of what the cap can do for you.
As I said, the back pressure from the (fully assembled) stock muffler may be a bit restrictive so you can try modifying it a little bit, just to improve the flow but leaving some back pressure.
It shouldn't be this difficult to get the jetting done.
And no I don't think it can be the fuel filter.
Certainly, I don't see any reason why it shouldn't be close to the carburetor. The lower it is below the tank, the more pressure there is to flow fuel through it anyway.