Obviously most of us don't have a mini excavator sitting around
We don't either. Rental on all equipment is figured into the cost of the job, along with delivery if needed. The only piece of equipment we own that is capable of pulling out shrubs is a JD 4300.
About the only ripping and tearing we will do, is if we will be re-planting the landscape. Only once in the last 2 years can I think of a job that was bid strictly as rip and tear, and that was actually in the last week. There's a chance that if we get that part of it, we will also re-install.
As for a winch, you will need a LARGE winch to be effective. Certainly not one that costs $50-60. To be effective, you would need a winch rated for AT LEAST 6000 pounds, and that may be on the small side. And that will cost you at least $500-600.
If there's a rental yard nearby, try either a mini-ex or simply cutting them with a chainsaw and grinding the stumps. If you are re-planting, make sure you mix in some fertilizer with the grindings, lest they rob the soil of nitrogen as they decompose....
About 3 weeks ago, we removed 18 large, overgrown arbs and viburnums in less than 3 hours using the cut and grind method. I don't think we could have done it much faster, but then again (as I'm getting a big ego boost right now), I think the experience of the equipment operator (me) played a big part...