First, don't bother with herbicides as they generally don't hurt the bamboo, but can do a lot of damage to other plants. Second, the advice of the American Bamboo Association is to keep watering it and cutting it down until you kill it by exhausting it, which supposedly takes a couple of years. I've never tried this and I'm skeptical that it will work over such a large expanse with such a well-established root system.

I believe your only recourse is further digging. I have a lot of bamboo around my yard, some with barriers and some without, When uncontained bamboo escape into my yard, my tool of preference is not a shovel. I use a pickaxe and start chopping with the pointy end along the line of survival shoots. Then I use the pointy end to pry the rhizome out. Sometimes, if I am in the middle of a rhizome, I just cut it in half and start working on each of the two pieces separately as it is easier to pry out rhizome that has a loose end. When I get a foot or two or rhizome out of the ground, I start pulling on it, and sometimes it sort of "unzips" from the ground for many feet. This is where it would help to have a friend with some upper body strength. Also be aware -- when wrestling out a piece or prying hard -- that you do not want to be off-balance if the rhizome snaps: I've had a couple of spectacular tumbles until I learned this. Because the roots are tenacious, prying them out will do some damage to the lawn. I always have some extra dirt around to fill in where I need to and to help the grass grow back.

I'm sorry that I don't have a magic solution, but at this point I think you'll just have to keep up your removal efforts. I think the other things you have done with trenches sound good.

A very simply solution is to get a decent sized steel broadfork, and a lopper which can eradicate a grove pretty quickly whether it is established or survival shoots.

I happen to use it for cultivating my garden beds, but I find that it can easily get chunks of bamboo out with surprisingly little effort. I use the 16 inch one from the following source which was strong enough to snap 5 inch diameter maple roots with a nice strong pull.

I'm not exactly sure if it would work just as well if you don't weight that much, but being 6ft, and around 170, this thing can get just about anything out of the ground. If I don't weigh enough, to lever out something, I can simply get a helper as this thing has 2 handles.

Here is a link that might be useful: example of steel broad fork

I've seen round-up works on some bamboo. At least it helps greatly.

achang-
You may have seen different results, but I have never seen Roundup being effective with bamboo. Even if the OP has some success using it on the current above-ground growth, this large of an underground field of rhizomes is not likely to be fazed by it. The only way to not poison the yard and be rid of the bamboo and rhizomes is digging, in my opinion.

If there was an easy way to control or eradicate bamboo with chemicals, people would not be posting all the time asking about how to remove it.

Here is a link that might be useful: Roundup and bamboo

This post was edited by kudzu9 on Mon, Jul 1, 13 at 2:19

And here is what the American Bamboo Society as to say about bamboo removal:

Here is a link that might be useful: Controlling bamboo

A small back hoe? Or save your back and save some money and hire labor to dig it out if you can't fit a small back hoe. At all costs, save your back! The right power tool can get a lot of work done quick! Good luck

Wouldn't continual cutting of the above ground growth result in starving out the energy stored in the rhizome system? Without photosynthesis it couldn't survive unless I'm missing something about the bamboo's magical ways. I'd think eliminating all top growth for a series of years would do it, but I don't have any firsthand experience doing this at all, just research.

You're correct. Clear cutting to soil level and mowing over will wipe out a grove no matter how big it is. It will likely come back with survival growth, smaller and smaller with each cut.

Some bamboos may be wiped out simply by the initial clear cut while others may hang on much longer.

What kind of bamboo is it? Just a piece of root sells for around $20. Sounds like you have an eBay store growing in your yard.
I would love to have a root cutting to try.

Pour boiling vinegar water on the area or even left over pickle juice. Kills ants, too.