A few thoughts.
Is it the width of your foot that causes the toe to hit the side or the fact that your foot slants towards the outside causing it to “find” the outside of the shoes? If that latter (generally some kind of forefoot varus), I have the same problems and have found getting some good foot beds helped a huge amount.
Also, is it all cycling shoes that give this problem or just Shimano. My feet are silly wide and Specialized seem a good fit for me.
Also (again), if you do go for the Shimano custom fit see if you can find a tame ski shop before you get them done, you may be able to get some padding or a long toe box from them as they will use them when fitting ski boots.
Finally, if you do have some foot problems (and it sounds like you might) then a trip to see a sport focused podiatrist may be an idea. Not sure where you are based, but there is a place called Solution 4 Feet in Bicester that are very very good at offering solutions for this kind of thing.