Just for the info stream here, forestry mowers produce chips on the ground which can be left as mulch. The one previously pictured would probably mow up to 7 inch trees. Guys in my area go out with that unit for $150 an hour. I realize you're beyond that.
You can recognize poison ivy etc right?
My eventual goal is to take it back down to ground level to reclaim the back yard - as in grass. Believe it or not there was lawn here once upon a time. If all this was reduced to mulch surely it would be a foot thick or more...?Just for the info stream here, forestry mowers produce chips on the ground which can be left as mulch.
Hmm. Looking at video on Youtube they look simple enough to operate and looks like it would be a lot of fun - I can see the mini excavator knocking down some of the growth - I don't think it would be appropriate for the largish trees which are still going to require some sawing - can't just knock them down since I have neighbors around me, and I might want to leave a couple standing - but then what? There would still be literally tons of stuff that has to be dealt with. I don't want any large trucks driving across my septic system which they would have to to get to my back yard.You can also just rent a mini excavator or skid steer, or even a mini, and just bulldoze it all. Be done in a weekend, including hauling it out.
looks are deceiving, but you only can learn by doing. If you aren't familiar with equipment this is daunting, but can be done. A tractor, backhoe, or skidsteer equipped with forks moves brush piles easily enough, not as good as a grapple, but it can be done. You can also just use the blade on a mini ex to just push brush to a spot where you can load. Using equipment like this is how most small jobs are done in construction, including pipeline. You would likely want a dump trailer as well if you have a decent sized truck, lower sides means easier loading. Just don't get the smallest machine possible to try to be cheap, bigger is sometimes better 
There's no way to avoid it. My septic system - tank and drain field - extends most of the length of my front yard and there are trees blocking any other path to the back yard which can only be accessed from one side of the house.Then don't have the truck drive over your septic
It still has to be moved to something, and that something still has to be hauled in and hauled out, across the aforementioned septic system.A tractor, backhoe, or skidsteer equipped with forks moves brush piles easily enough