I have no experience with gluten-free flour, nor (much) with cake making. But from a process/chemistry point of view, if you feel the liquid has settled to the bottom, maybe it has. And what might help in that case, would be to bring the egg mixture up to temperature a bit before you fold it in the flour and put it in the oven. Wikipedia says egg coagulates starting at 144F, so keep it below that. Microwave at 30% power might work if you nuke 20s then stir then nuke 20s then stir, etc. Thermometer helps.
The idea being, that if the egg is warmer, it'll coagulate sooner as you put it in the oven, and therefore capture the liquid before it's got time to sink to the bottom.
THAT SAID, I am aware that baking cakes and cookies and such really is one of the higher sciences in cooking, and without much experience in those (I'm just not a big fan of sweets), maybe this is really stupid advice. On the other hand, afaik the proportions of ingredients are most important with these recipes, and I don't see why the process of heating and baking would not adhere to my laws of common sense
So I apologize if this advice ruins a batch of your ingredients.