I just sort of figured that heavy MTB shoes are the price you pay for a gravel bike.
I wouldn't be opposed to my Carbon Look Keo's and my correspondingly light Bontrager Classique's on gravel rides if I knew I'd never have to stop.
The run of the mill Shimano MTB with carbon soles work for me. I think they're fairly expensive new but can frequently be found in a Co-op or eBay with one single scratch for under $35. I've gotten two pairs this way.
I won't ride a shoe with discernable flex. I don't pay attention to stiffness rating but carbon seems like the best way.
I also ride single sided Exustar. They're basically SPD but lighter.