You're already onto some of the labor saving tips to help you. the lilac can be difficult to transplant since the root ball gets exponentially larger with increase in bush size. Fortunately, the seven footer should only have a root ball about 2 1/2 to perhaps 4 feet in circumference. It won't have a tap root, but you can expect to find several shoot coming up near the bush's base. Prune, as you've suggested, back to about 4 or 5 feet, removing several of the crossing branches in the middle and try to visualize what the bush will look like once it reinvigorates. The pruning and transplanting (for this purpose) both need to occur during dormancy. I would attempt it in early spring before any new growth appears. Once the bush is extracted from the ground, prune away any damaged parts of the root ball and try to loosen the ball somewhat for good water circulation after replanting. Be sure to make the hole for receiving the bush large enough for the roots not to be compacted. In fact, I've made the holes at least 6 inches to large and then lined the entire hole with peat moss. After resetting the bush and back filling with fine dirt, water profusely to wash dirt into the root ball trying to prohibit any airpockets. Water at least everyother day for a week or so, but not so much that the plant is standing in water ("wet feet"). Work in a little rose plant fertilizer (low on nitrogen) since excess nitrogen inhibits blooms on the lilac, and mix in a little (maybe a cup full) of lime since they like a slightly alkaline soil...pH of 7 is ideal. Next season, be sure to prune right after blooming is finished to encourage blooms for the following year... Best of luck!