How to make a custard (royale) that sets up firm on the stovetop?
A custard royale is not stirred during cooking, this leads exactly to the scrambeled eggg effect you had. This is fundamentally different from the standard custard process you are probably familiar with.

The (preheated) cream is mixed with the egg and/or yolks, then put in the vessel it's supposed to be cooked in.

It can be cooked over barely simmering water or in the oven in a bain marie at 90C. You simply give it enough time to solidify, which may be somewhere between half an hour to almost an hour, depending on the thickness. Cooking in an oven tends to take a bit longer than on stovetop.

Let cool completely before unmolding and cutting.