OK its time for a lesson from the old master:
First the fall on plumbing drains should be at least 1/8" per foot and a maximum of 1/4" per foot. You say the drain is 60' long; 60'X1/4"=15" total fall for the drain. The reason for the min/max fall per foot is to keep the solids moving without the water running off and leaving solids behind. This was determined by extensive testing by old timers. In hard ground you can put your drain rather shallow under the slab keeping a proper fall; then, when you get outside the building line, put in a test tee and drop on a 45 degree angle so you will have 18" of cover over the sewer and then carry your proper fall on down, using the backhoe (save your back).
For the shallow run in the building line, you may use wyes to join fixture drains to the building drain; otherwise, if you use tees they must be laid on their backs or no more than a 45 degree angle, never lay a tee on its side. That gets you to digging too deep in the hard ground by hand.