Baked Rum Custard, As Eggnog Base

This is the first occasion on which I can remember having posted.

Essentially, I am after a recipe for a baked rum custard that I can use as a base for eggnogs. There are two conditions on this recipe.

The ethanol in the rum, the substance that causes intoxication when consumed, has to be completely burned away in the baking of the custard, which I know cannot be done without baking it for extended periods. That is the first condition. It is in place because the eggnog that will be based on this custard will be served to persons who are not old enough to drink liquors legally.

The second condition is that the total yield quantity has to be large, with a capability of serving more than ten people at a time, for the eggnog that will be based on this custard will be prepared in quantities of more than one American gallon at a time. IT is in place because the eggnog will be served to a large group of people, and I want them to be able to return for more than one portion of it.

Any assistance given along these lines will be greatly appreciated, and those who provide me with such assistance are hereby thanked in advance.