I have the same issue. To get it to fill I have to hold the hose TIGHT on the hole once it gets to the point where it tries to come back out. During fill up when it goes in ok I run inside and turn the pump on (once enough is in the tank the pump doesn't run dry). Once it acts like its full I run water using the outside shower while holding the hose TIGHT to the hole, after a bit water will SHOOT out of the vent tube and it will begin to fill normally also pushing air out. I can hear the air coming out of the vent tube. I have a task to take the side wall out of the basement storage to look at the vent tube. I suspect the vent tube hangs lower than the top of the tank letting standing water into the tube.
I don't know if running the pump to get a little water out helps but it seems to.
If the vent tube is blocked the air being pushed out of the tank when you fill it has no where to go.
The linked fillers will not help as this is a vent tube problem. The tank is pressurized due to the vent tube having water in it and that makes it act like its full after filling for like 4-5 minutes.