The $24 question for me...

[Michael Hopcroft]

Is whether the same modules work on other 5e games and settings, such as Everyday Heroes or Doctors and Daleks, and whether the systems needed to play are at all altered when you have different subsets of rules. What can be handwaved in?

[Zacchaeus]

I'm not really sure what the question is here. I can't find either of the systems that you mention on the store or on the forge so I assume that rulesets for these systems don't exist but that both are based on the 5e ruleset?

So whether the 5e ruleset as it stands can handle such games will depend on how much of a difference there is between the systems and the existing ruleset and how much you want to closely match what the changes are. For example if there are different skills or the ability scores are different or combat is handled differently. If you want to closely match these systems then you'll either need to create a new ruleset based on the 5e one or write an extension that handles the differences.

It's difficult to give more precise advice without knowing what differences there are in the systems you mention and the current 5e ruleset.

[LordEntrails]

Have you tried installing the free demo of FG and creating a campaign and seeing if it works for you?
Note, FG is powerful, you should read the user manual or perhaps even take a free FG Academy class to learn enough to know if you can make things work for you.