I understand disliking chemicals, but perhaps poison ivy should be the exception. Personally, I'd go that route before I invested a lot of money in equipment that has very limited use.

Is this an area that you plan to garden? If it is, go ahead and plow, rototill, or whatever and then see how bad the roots and rocks are. If you are just trying to eliminate the poison ivy and honeysuckle, get roundup and spray it. NOt the environmentally best idea, but it works. IMHO honeysuckle and poison ivy are very difficult if not impossible to eliminate unless you get the roots out AND plan on continuing doing that for years to come. e.g. I have an old fence on the road in front of the house which is totally covered with honeysuckle. The garden is about fifteen feet from it with lawn between. Every couple of years I "chisel plow" with a farm tractor a couple of times through that area ripping out honeysuckle roots. They migrate under the lawn and then steal nutrients from the garden, lawn too I guess.

Also, a rock rake is a "wonderful thing," After the initial use how often will you use it? I have a barn full of "wonderful things," :-) Think about that for a bit.

You could also try researching what type of soil the invaders like and add amendments to make it unpallatable to them. e.g. I started having wild onions appear, researched and discovered they don't like high PH soil. Limed the area very well and a year or so later, no wild onions.

Good luck,

Ev