Get a hot knife and start carving on those muds. Don't slice on the outer lugs, though, to avoid chunking later on. The crosslinked tire chains will create less driveline stress and vibration, and give better side-hill traction. If possible, get chains with the cam-locks on them. They keep chains really tight, which is a must when wheeling. I love chains. They're great for traction on the slippery stuff, but I love low pressure more. Try both.
Also, I usually run my chains in the rear, and they work fine. I just don't have enought fender clearance at full lock to clear them in the front.