Utility engineer here.
Find a new contractor, yours is working with the tools they have have, but a specialist will be able to cut the roots that have infiltrated the pipe, then run a structural epoxy liner through the old one (called CIPP).
Tree roots look for oxygen, so once you have a solid cured in place pipe, they’ll grow around it instead of trying to intrude.
From an arborist perspective, usually limiting the trenching to 30% of the root zone (a radius based on the drip line of the tree) will leave keep the tree alive, but it’s still a gamble.
The 30% will include the arc of the circle it cuts off, and if the tree is large enough that it could fall on a house, it’s not worth the risk.