I had missed commenting on one thing in your question - you mentioned totally relandscaping. Because there are going to be roots all over the place, and they sprout new plants off the roots all along the root length, any excavation, tilling, moving of dirt, etc you do in the yard will have those new plants and roots, and will start growing again. Therefore, once you poison the main plant to kill it as much as possible, the only relatively safe way to landscape would be to remove as much dirt as you can afford - preferably a foot or so (and dispose of it at a landfill, NOT on-site or be trucking to someone else's yard job), pull up as many roots as you can find, spray the entire area with kill-all type Roundup, and bring in new material (general fill + topsoil) to cover that area - hopefully burying it deep enough it will die before working up through a foot of soil to find sunlight. Then do not plant anything expensive or deeper than annual flower seeds or grass the first year or two, or their roots will hit the Roundup and die.
Of course, that process costs more, and is no guarantee some rootlets will not take hold and grow in the new material and make it back to the surface. By making the new material crushed rock or washed gravel except for the top 2-3 inches of topsoil you can make it hard for it to regrow, because the material in direct contact with it will not be good growing material. Be sure to use landscape fabric (biodegradable) under the topsoil to keep it from washing on down into the general fill for a year or so, so it does not feed the bamboo rootlets.
Of course, if you have tree roots in the same area and you want to save the trees, this is not going to be good for the trees - especially if you cut major roots or use the roundup.
Before getting started, I would curl up with a laptop or iPad and do some serious web browsing through the articles you find with this search phrase - killing bamboo
Get a good feel for what has worked for other people, and I would really recommend trying the poison route this year, and wait till you see if it pops up again next spring before going into an extensive relandscaping project. It may well take through next year with repeated spraying or painting of roundup to truly kill it off - and that assumes you can kill it ALL - including any that grew into your neighbor's yards.
I personally would not hire someone to do this - because of the repeat application nature, this is more a do it yourself job, except for rooting out the remaining trunks and major roots once dead (and be sure to warn them about the roundup use, so they wear gloves).