"Massive challenge" might be bit of an understatement for those of us with high volume feet looking for cycling shoes. Particularly on a bit of a budget. Legend has it ultramarathon cycling god Lon Haldeman set transcontinental records riding in wingtip dress shoes because his cycling shoes hurt so bad as his large feet swelled after a few hours. In the early days of SPD pedals, many made shoes that fit from hiking shoes or winter pack boots with cleats bolted to the sole. So think outside the (toe)box and make your own-make a cutout in the sole, drill some holes, get some t-nuts and attach the cleat of choice. The adjustment range for cleats on the average cycling shoes is too narrow and in the wrong place anyway-many well known bike fitters do this modification to cycling shoes to make their clients comfortable and injury free. Find a trail shoe that fits, with a 3/4 length re enforced last and sculpt away. Ride serene and free! Power Grips and toe clips CAN STILL be purchased if comfort over rides the ego. One of my attractive cycling friend's rode her stunning CFMP with the six inch heels removed and cleats attached. She wasn't the only one that thought they looked good with lycra!
From your description, it sound possible that volume rather than width is the real fit challenge for you. You might check out some of the different shoe lasts from Shimano's new product line. Some have taller, higher volume toe boxes, even in regular width and some models do come in wide. Some also have an extended cleat mounting range. Some people suggest Shimano shoes to be the best cycling products they make. Sidi Mega shoes can fit well for many cyclists with higher volume feet. Certain models of the Pearl Izumi Alps range have had more forefoot volume but it varies from year to year. Lake can make some fine shoes but sizing and availability have been difficult, even pre supply chain disruptions. Some years wide shoes are available across the range and some years not.
Depending on the material and the construction, it is possible to "stretch" some shoes. Find an alpine ski shop, skate shop or western boot shop that has a proper boot press. With the right tool and some experience you can do amazing things. We sold a ton of ski boots in our shop because we could guarantee a comfortable all day fit.
Good luck finding "Happy Feet"!