Bunch of things, hang tight.
You mention HVAC. These systems frequently use the basement as the return air source for at least some of the return air. The basement air is usually higher in radon. The HVAC system spreads this throughout the house if it draws any air from the basement so your 3.8 may be the same throughout the house.
Bigger Fan. This generally makes sense, but not always. We sometimes see a bigger fan raise the indoor radon level. This is because of pressure gradients. It is the pressure gradient that "causes" the radon problem. I'm from Maine. Indoor radon levels are usually higher in the winter when the heat is on. This is because hot air rises, decreasing pressure in the basement, the furnace uses indoor air for combustion and sends it up the chimney further decreasing basement air pressure, any exhaust fans (kitchen, bathroom) decrease indoor air pressure, clothes dryers typically vent outside and decrease indoor air pressure. People usually seal everything above the ground carefully to try and decrease any cold air infiltration so the house is left with the ground level or basement to get it's make up air and it sucks the radon right out of the ground. So you need to carefully seal the cracks or penetrations in the basement before you finish it. The floor is poured after the walls have dried so there is a "cold joint" between the floor and wall this needs to be sealed. If the basement isn't well sealed the bigger radon fan may decrease the negative indoor pressure by sucking more air out through the basement penetrations. Good radon diagnostics can determine if your "pressure field" below the slab is distributed enough to cover most of the slab. A bigger fan may extend that pressure field but an additional suction point might do it better. Good radon sealants (caulking) say they are designed for radon or they are urethane or polyurethane based and are frequently called adhesives.
Guideline levels: the EPA and WHO levels you mention are correct, but these levels are based on year long average radon concentrations. Most people base their decisions on a two day test. You are alarmed by the fact that sometimes it goes above 4. I just wanted to point out that the guidelines are usually misapplied. You know a lot more about your radon level than most people. Additionally, I should point out that we have a lot of data that tells us a radon mitigation system that is installed correctly (ASTM standard 1465) will get your radon level down below 2. There are naturally unique situations where this is not possible, but mostly it is.
Standards: the ASTM standard is a withdrawn standard, this means that ASTM has not updated it in more than 7 years. They are waiting for the industry to develop their own standard (which they have).