I don't make mud cakes, but I use custard for fillings and am a big fan of German buttercream which uses custard as the base for the European buttercream.
First, you can add as much as 50% more (but 30% is fine) cornstarch in your custard with no flavor change. You can even use cornstarch in flour based recipes.
Many bakers do not take the custard to the optimum temperature and this will affect the thickness. Use a thermometer and carefully bring the custard to over 160 degrees (needed for egg safety anyway). Then wait for the custard to make the big "burps" of bubbles. Then let this action happen for one minute. The custard is now cooked.
Another method is to use a hand mixer instead of a whisk or spatula. It is amazing how much more thickness you can get from the same recipe.
Using one, two, or all three will help you control the thickness. This is how I do my GBC. GBC is like IMBC, SMBC, and FBC, but the base is custard. You pour the hot, completed custard in a mixer and mix until it gets to room temp. Then add the butter like the other European buttercreams.