So I work for a company that manufactures monomers, and just had a bit of additional extra training on this precise topic of stabilizing double bond containing reactions
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Two things: you should consider adding phenol inhibitors like BHT, MeHQ, etc, and also possibly phosphite inhibitors to consume peroxides. Additionally, consider actively sparging air... that what is done industrially when doing something like esterifying acrylic acid. The bit of water that gets in doesn't matter because you're azeotroping it off anyways.
Fumaric acid is just plain more radically reactive than maleic due to the electronics of the cis vs trans double bond... though it should be said that at raised temperatures they will interconvert. I forget what ratio you end up with and how long that takes to happen.
The alcohol really shouldn't affect things too much, unless you're comparing primary, secondary, tertiary, or you have a volatile alcohol that likes to boil out. Phenols also won't react well under Fischer esterification conditions.