I did something similar but not as drastic when I had a TT and had the same results. I installed a 175# welded platform loaded with a 163# genset on it. On my test ride I had some wiggle/sway and I was using a Hensley hitch.
Using a Sherline tongue scale I reloaded my cargo to increase my tongue weight.
I had a 4 bike rack mounted on my tongue, and shifted all my heavy items to the front storage. I kept my TW between 1250# and 1300# at all times and my sway issues went away.
Keep in mind this was on a 11K GVW 36' long TT with a substantial 10" I-beam Frame. This was an old school stick and tin trailer nothing light weight about it.
I had no further issues after balancing my cargo. I towed all over with the genset on the rear for about 3-4 years.
However I was only dealing with 400 pounds off the rear not 1000! I'm not sure I could have over came 1000# and maintained proper TW. I'm also not sure my frame could have withstand the stress of 1000#.
You will at least need to get a tongue scale or plan to spend a few days going back and forth to the CAT scale in an attempt to find the correct balance and TW. Even then you need to ensure your frame won't be over-stressed.