Alee,

Do you use temporary sprinklers or are they in the ground and permanent? Are they run by an automatic controller? Soaker hoses on a lawn are cumbersome and unsightly. Soaker hoses need to be pressure regulated same as drip lines. Is this your backyard (100 ft x 20 ft)? What type of grass are you growing? The grass dying back around the tree make not be just a watering problem but a shade problem or a lack of nutrient problem. Aloha

Soakerhose is not really meant for lawns. If it clogs, then you have to dig up your grass to take it out. Netifim has a hose for lawns, and can be buried.
What about just setting up some micro sprayers? Of course you would have to move them when it came time to mow! They don't put out as much water as a sprinkler, so you shouldn't have run off issues with them.

Just my 2 cents worth....good luck!