cssharpe5097, just my advice if you are interested. I have a similar situation as you do however it's not a mile long, more about 1/4 to maybe a 1/3 of a mile. My 'swampy' area is not swamp but deep peat and thick with cedars, white cedar, poplar, red maple, some elm and ash. I was also in your position last year and hired a dozer guy to come in and make a trail through it after I had cut everything down and move all the logs/leafy material out of the way. All that was left were stumps. The guy said he could do it in a couple days and that he wouldn't get stuck which was my big concern (there is no way to get big equipment back there). So he tried and failed and nearly got stuck. So he backed out and at least was savvy enough to know when he was defeated. So this past August, I went in with my old
B20 tractor and pulled a number of stumps out of the way (mistake on my part, should have just cut them to ground level) with the plan to go with a corduroy road. The reason for me going this way was that I dug down in the peat to determine depth and possible fill required and some places were 24"+ so that was out of the question as cost would be prohibitive. So far I have the corduroy road only about 150ft in but it works really well for my needs which is getting my 7000lb tractor to the rear of my property cut trails and just manage the back part of the property. Now I am doing this currently all by myself and have given myself 10mths to do it as I know it's going to take that long. I could hire a few guys to come in build the corduroy road which is another option but I'm going to have a hand at it myself as I enjoy doing this type of work.
As for the equipment you are asking about. I also considered a dozer initially and then had nightmares of getting it stuck back there with no way to pull it out. Note my trail is not going through swamp, just a low area that collects water in the spring but the soil content is such that it will not hold a lot of weight. I then thought of buying a used excavator, a big one, that I know could do the job faster and easier than I am doing it. As a newbie with that type of equipment, I could see myself getting it stuck as well and that would be worse than a dozer. I know they can get themselves out of places much easier but perhaps my lack of experience would prevent this. So then I thought of a mini-ex which is what you are currently thinking of. Luckily my Kubota dealer was nice enough to loan me one for a long weekend, KX91, and it was a great machine. It plucked out trees and had a thumb so I could pick them up and move them but it also was heavy and started to bog down in the trail as of course it rained heavily on the weekend. So while it probably could have done the job well, it was not the solution for me in the end. I would consider renting it however as I plan to cut a lot of trees this winter for the corduroy road and then continuing in the spring and it would come in very handy to move the logs into position (been doing it by hand and it's tiring work!).
I guess I am saying is I understand your dilemma and your desire to do it yourself. You do need to do some careful thinking of what makes sense for you. Based on your desire to get an ATV back there, I would go the corduroy road method if it was me. Also if you buy or rent a mini-ex, make sure it has a hydro thumb. Good luck!