Bob,
You've got a tough situation. It really sounds to me that bentonite, in your case, is a very high risk of not fixing your problem. Those tree roots and associated 4 leaks have got to be repaired; bentonite will not do that in my opinion. For bentonite to have any chance, you will have to drain, apply, and mix in the soil. That is not a weekend warrior job and you will need some heavy equipment.
The liner sounds like your best option, maybe only option if you are positive you can not get a dozer in and haul in clay to fix the problem.
If it were me, I would look real hard at bringing in the dozer....as Gator said, the dozer will make its own path and can also make a path for dump trucks to haul in good clay to fix it right.
In any case you are looking at significant costs. Your cost potential tells me that you should bring in an expert...an engineer with a good reputation that can develop those trades for you to consider.
I've never dealt with liners and just can't offer advice in that regard and my experience is with clay embankment ponds. Hence, I am admittedly biased toward the clay approach. It will cause some disruption to your property, but that can be minimized and in a few months will be back to normal.
My best advice is to get a professional engineer in to give the options and the costs associated with them....but I would be very skeptical of bentonite in your situation.
Keep us posted, please.
