Thanks for the advice, all. We have visited Madrid a few times and really enjoy it, and Spain in general. But in this particular situation, getting to our destination as quickly/efficiently as possible is the priority.

I wound up cancelling the IB award and rebooked a different award with LH in business class with a 90-minute connection time in Munich, which is typically a breeze to connect. On the bright side, I received both the Avios and fees refunded in less than 48 hours.