I think in general a "feeling of happiness" because it is a feeling is well within the category of pleasure. It's when people start to embellish "happy" with all sorts of other definitions that are not feelings that the problem comes.
I just feel like this hypothetical is in the realm of it being entirely implausible given the particular parameters. Its an idealist abstraction that doesn’t take into account reality. How reality works, how nature works, how human behavior works.
And I think you are describing Platonism / Stoicism / virtue exactly: "idealist abstraction that doesn't take into account reality, how reality works, etc.