Does it make sense to follow an adjective phrase such as "however difficult" with the modal auxiliaries "may/might"? Isn't it a bit pleonastic, since "however" already contains the idea of either uncertainty, or irrelevance?
"However wealthy he was / However wealthy he might have been, she would not have married him if she had not been in love with him."
Does "he was" imply that his wealth was certain but irrelevant, and "he might have been", that it is/was a matter for conjecture and irrelevant, anyway?