Wide Cycling Shoes

My cycling is blighted by my feet going to sleep because the footbox of my shoes is too tight. I have short (size 41) feet that are wide at the toes. Like a Hobbit but not as hairy.

I am wearing cheap Shimano R32 SPDs because I didn't want to spend too much on my first pair of shoes. I want to move over to SPD SL shoes because I think they will offer me a larger surface to press down on maybe stop my feet from falling to sleep. But it might be the width of my shoes. It feels very tight against my little toes and my feet fall asleep. So I'm not sure whether it's the cleats and their small surface area or the narrow shoes.

The only wide shoe I can find is a Shimano R088 wide version but that only starts in a size 42.

If you're 100 per cent sure you have very wide feet and have had problems with shoes before changing models would you mind letting me know what shoes you've moved to? I don't want to spend more than £75 and I'm not bothered how inflexible they are. I just want some comfort on my bike.