It sounds to me like the other managers don't believe that the metrics you are using will result in higher productivity faster. This could be because they just don't understand or haven't fully internalized the benefits of passion etc., but I suspect it's more likely that they're feeling the pressure to higher someone, anyone. Assuming you have enough autonomy on your team to make a hire based only on the merits you list above, have you been able to demonstrate to your higher-ups that your method is more effective? If the higher-ups understand what's better about your approach and that other teams aren't following it, they may be able to start changing the culture or putting pressure to change interviews.
I'd also recommend re-examining the "must be better than the last hired engineer" point. Different engineers excel in different areas and I suspect you'll run into problems like "well they're much better at algorithms than the last hire but they didn't ask the requirements questions I'd like", etc. To me it seems like a weak link that your peers may focus on to the detriment of your other goals.
Again, not a team lead, just suppositions and suggestions based on the engineer side. Mostly just sounds like a company culture issue, gotta make the superiors understand why haste makes waste.