Hi Bulldog,
I'm not a fan of herbicides and chemicals so I tend to go with the most environmentally friendly methods first. There are stump removers for the large stumps, but it sounds like you won't be needing those.
Honeysuckle popper, Bush and Shrub removal without a back breaking garden shovel - Mister Honeysuckle Weed Wrench The next tool I would use would be a radiant heat weeder. I think there is only one company in the US that sells them, but I'd also look to rent one if possible.
Radiant Heat Weeders If the area is not vulnerable to fire, a flame weeder might be another choice.
http://www.pesticide.org/pubs/alts/pdf/flameweeding.pdf For spot spray I would choose horticultural vinegar as an herbicide.
Spray Weeds With Vinegar? / May 15, 2002 / News from the USDA Agricultural Research Service As already suggested, mowing should also be helpful depending on the particular invasive.
I would also suggest keeping a stirrup aka scuffle hoe, collinear hoe and/or circle hoe on hand for touch ups.
Old-House Journal Magazine Newt