We've had some excellent investigative work and good feedback, but no-one has explicitly responded to the core question
"Shouldn't we have migrated the question to English.SE?"
I'm game. It would seem, based on the advice in [@gparyani's answer], that the logical answer is
"Yes [we shouldn't have]."
If flagging as "off-topic, migrate to EL&U" is almost certain to result in the system automatically rejecting the migration because of the tag issue, then this flag option is useless and we should stop using it. More pertinently, we should ask that an appropriate fix be applied - for example, integrating the same mechanism that works for moderator-assisted migration. I didn't understand the suggestion in the MSE comment about "intrinsic tags" but this seemed like another potential solution. If for some reason a fix isn't possible, the only remaining solution is for the "off-topic/migrate to EL&U" option to be removed.
Unless/until the flag mechanism can be fixed, I suggest that questions suitable for migration to EL&U should be flagged "in need of moderator intervention" with an explanation along the lines of "off-topic but suitable for migration to EL&U".
Assiduous users could also post a comment on the question itself explaining that it's off-topic but has been flagged for migration to another SE site. I'm in two minds whether it's appropriate to say explicitly that it's to EL&U, as the OP is then just as likely to go and cross-post to that site; this can be messy, as it then requires another process on EL&U (assuming the question is successfully migrated) to close the migrated post as a duplicate of the cross-post.
If it's been flagged for moderator-assisted migration, I think a separate VTC for "off-topic/what-to-write" or "off-topic/blatantly-off-topic" (depending on the nature of the post) is still necessary, as the primary objective should be the integrity of this site rather than where the post might go. But I'm not sure on process: can you do it in this order, or do you have to VTC first then raise a moderator-intervention flag?