Stop thinking in terms of a rate for a bobcat with operator or a sawyer with saws and start breaking things down into labor, small equipment, big equipment, overhead, mileage and profit.
1) Labor: You said one week. If that means 40 hours and each of you (you and your wife) wil be working 40 hours, then 40x2=80 hours. Assuming you won't have any employees other than yourselves and no taxes, insurance or benefits to pay out, you just need to put a price on your labor. If you want to each make $15/hr, then $15x80 = $1200. Bear in mind, your going to have to claim your income (and expenses) on your taxes. No freebies - especially if the state will be aware of your work on the job.
2) Small Equipment: Saw maintenance, cost of oil & gas, chain maintenance, etc all costs money. A rental store probably gets around $75/day for saw rental. Say you're going to use your saw a total of 3 days (cleaning up debris the other two days), then you should charge around $200 or so for small equipment use.
3) Big Equipment: What's a bobcat cost to rent? Around here, one with a grapple costs about $200/day with a grapple. Say 3 full days with bobcat x $200 = $600. What about a pickup and trailer to haul equipment? 5 days x $50 = $250. Mileage???
4) Overhead: If you have absolutely no overhead, you might want to think again about doing this job. Does your homeowner's insurance cover you for any fire damage should the burn pile get out of control or your equipment spark a grass fire in the CRP? So, what will a rider on your insurance cost to get you coverage?
5) Profit: You don't necessarily have to make a profit if you're not really looking to make this a regular gig and if your pay is included in the labor calculations; however, it might not hurt to add a little something for the unexpected - a cushion persay.
Add it all up and I see a number somewhere around $2250 minimum just to cover basic labor and expenses. I think your biggest concern is liability. Make sure you have some kind of liability coverage in place or you could really wind up in trouble if you inadvertantly burn things up and get sued by the state for wrecking their leased property while maintaining it for the owner!