I prefer a wide toe box when running (think Topo or Altra if you know running shoes). With cycling, I tend to get foot pain unless I loosen the shoe straps. I’ve had good experience with Bontrgare XXL, which seemed wider, but they seem to have changed that now.
Any recommendations?
Yes get fitted for some Lake shoes.
I run in Altra Lone Peak 7, Torin, Via Olympus and Hoka SpeedGoat wide. Also wear Vivobearfoot and Altra Lone Peak Allweather also Barefoot socks.
For cycling I have Lake in a wide fitting. The CX241 might be a good option they do also have a size guide fitting page online but if you can get into a stockist and try some that would be better. Size Guide – Lake Cycling NL
I have a wide forefoot and a narrow heal and have always had challenges with fit. I have found that in running shoes, the Hoka Clifton and (surprisingly) the Salomon Speedcross series have been great. I used the Sidi Genius Mega for cycling for a long time and then last year tried the Giro Empire SLX lace ups. They are great. My first real cycling shoes back in the late 70s were lace up leather and I never had an issue with them; the new Giros are reminiscient of those for me. Every foot is different, of course, but in general I would look towards a shoe with a more forgiving upper and don’t discount lace up. The last resort is to go full custom. I have been telling myself to do it for the past 30 years, but I just can’t quite swallow the $2000+ …maybe this year.
Third for Lake. I have MX238s and they are hands down my most comfortable pair of shoes including trainers and Birkenstocks.
You might be a candidate for one of the heat moldable Lakes.
True. My only issue with Lake was that I found the heel pocket a bit wide. But when I am ready again for new shoes, I’ll certainly consider them. 5 years ago, Giros did not come close to fitting my feet, but now they do, so I always keep an open mind when shopping for new shoes. I used to run a lot more than I do now, and given my strange foot, I was always excited to find a shoe that worked well…then I would go to get a new pair (or 3) and the brand would have changed the model. Thankfully cycling shoes tend to last MUCH longer than running shoes. 
I have the same situation as well as a tall heel. I am a repeat buyer of Shimano wide fitting. The S-phyre are really nice but the 7 series are almost identical in function and half the price. I couldn’t get on with the Giro Empire SLX lace up because they were WAY too narrow. I had a pair of Fizik R1’s which were like wearing slippers but the heel cup was too low.
I will look into Lakes when I get another pair.
I’ve been looking at this myself but hard to spend the money as not able to ride as much and thinking some winter boots would be a better option.
Good to hear about the Shimano Wide had thought about trying them but finding somewhere close to try them on was a non starter as no one seems to want to stock them.
Some awesome info. I thought it was just something to put up with. Glad it seems a common issue.