…I’m left with a strong inconclusive as to whether it’s possible :(
Possible, yes. Possible with current technology and understanding, no.
The methylation of DNA and other ways that its functionality is modified is something that is studied in epigenetics. Such modifications can also be carriers of heritable traits (ex. a study on Icelandic families found that experiencing famine could change the likelihood of diabetes two generations later). Modifying methylation has also been investigated for treatment of genetic diseases.
Conceivably, epigenome editing could be used to modify the sperm/egg methylation to make them compatible. But, that’s probably a ways a way from being practical.
Progressive relaxation. Seriously.