I doubt if you'll get that load 4' off the ground with the #70 loader. But you might get it a foot or two. Considering the weight, you might not want to lift the load more then a foot.
If you're using bucket forks (forks clamped to the bucket), that will really lower the weight capacity. I don't think I'd try anywhere near a 1000 lbs using bucket forks. If you're using the Deere forks (or equivalent) that replace the bucket...then I'd give it a try.
Make sure you increase your tire pressure to the maximum! There's a good chance a front tire could roll off the rim when making a turn. If that happened...at least is would be a real hassle, at worst it could roll your tractor.
Also, a thousand pounds is getting near the upper limits of the front axle capacity...something to think about.
What kind of rear ballast are you planning on using? I don't think filled tires would be adequate.
If you have a trailer you can hook to your draw bar, towing the load might be something to consider. The only difference I see is you'd have to stack your wood after the move.