Your tire clearances will show up at your front tires when you make turns and/or if you are off camber making a turn. You may get some front tire inner fender rub. This 'could' cause a problem if your fender wells are on the small side. I am unfamiliar with your rig. The other issue you will probably notice right away is a reduced amount of acceleration from a stop. You are essentially changing your gear ratio by installing a taller tire. Taller tires equal more linear footage per revolution. In other word it take longer to make 1 full revolution of the tire. That is the down side, on the up side while at highway cruise speed you should notice a slight gain in mpg since your engine rpms will be slightly lower at the same cruising speed as with the standard size tire.
There are some inexpensive options available to you to resolve the leveler clearance issue. If you have leaf springs, you could add a helper (over load) leaf to your rear spring pack, you could add air bags to your suspension, or if you already have an overload leaf on the rear axle you could add a set of upper Stable Loads from Torque Lift. there are some other companies that make this same bump stop. I installed them on my suspension and they lifted my chassis close to 3" and took out almost all of my side to side sway and added a touch of negative camber to my front axle which helped in steering control.
You could look at a small 2" or 3" lift kit for the Ford E450 Chassis. If you are mechanical these are typically simple installs and will freshen up your suspension. There are many other options out there, but these are a few suggestions to get you looking and thinking in the right direction.
The previous comment regarding larger tires with duals is due to issues with rocks or other debris getting caught between your rear tires or if there isn't enough clearance the tires could rub against each other at times of heavy loading which will increase your tire temperatures and heat kills tires.
One last note regarding load capacity. As with all tires, be certain that the new tires have at least the minimum manufacturers load carrying capacity rating for your rig. I always try to get the maximum load capacity tires I can get on my trucks. I prefer over kill because all it takes is that one time being over your rated capacities (tires, wheels, axles even chassis ratings)on a long trip when you could get yourself in trouble. Without over doing it, more is better.
Good luck
2008 Host 300 Super 'C'
2008 Ford F-550 Chassis
Diesel
4x4
Lariat crew cab
20' enclosed car hauler/garage
'87 Jeep rock crawler
Turbo'd