I agree with the others about moving the frog, but disagree about not filing. Stanley #4 planes are pretty common so you are not messing up something that might end its days at the Smithsonian. There is nothing sacred about the mouth and filing allows you even it up a bit. The original Stanley blades are 1/16" or less in thickness. This is a marginal size and leads to chatter. Thicker is better, but as others have noted, twice as thick can cause problems. I make my replacement blades 3/32". That is 50% thicker to control the chatter yet still thin enough to not cause problems with the mouth or with the adjuster. Sometimes it is necessary to file the mouth a little in front. Not alot, but about 1/64 or so--just enough to let the chips clear.
Here is how you do it. Adjust your frog back as far as you can. It needs to support the blade, but does not need to be exactly flush with the back of the mouth. Install the blade and check for clearance. If you still need some room, use a thin file running parallel to the frog bed and file the mouth evenly all across. You will probably find that your first file pass evens up the mouth. Check your progress by reinstalling the blade and looking at the clearance. Sight down the blade length. You need to see light that is about the thickness of a sheet of copy paper. File and inspect. Make sure you file evenly and make sure you file parallel to the frog--not perpendicular to the sole.
When it starts looking good, start testing with light cuts on scrap. At some point, things will come together. I like to use clear construction lumber (2x4 or 2x8) scraps for testing. The pine is easy on the blade. Once you are able to pull long shavings that do not clog, you are done. Less is more in this case because you can always file a little more later if it is necessary. Good luck.