Seems to be a general problem with the unsuitable plugs.
Nevertheless, using an external switching stage is a fool's errand. The FETs installed on the board are good for 50A, i.e. at 12V for a heating bed with a maximum of 500 watts (with some reserve), at 24V for 1000 watts (theoretically).
It makes much more sense to either solder the supply lines directly or to use proper connectors (XT60 for example). Then remove the paint from the two conductor tracks on the back of the board and reinforce the conductor tracks with a lot of solder and a piece of bare wire. It is also helpful to use thermal paste sparingly between the FET and the heat sinks.
Then there will no longer be any problems, even with thick heated beds...

But of course that's just my personal view of the matter...

Greetz
Micha aka CBX.Micha