You might be right, but for what it’s worth I’ve literally never heard any of those words pronounced that way. I’ve only ever heard the word “English” start with the same sound as inside, while “engage” and your other examples start with the same sound as entertain.
While you're right, I feel like there's no safe argument to make here, because some group somewhere will pronounce some word in a certain way, so there can't really be a blanket rule.
