Dragon; you are correct I miss spoke.... please exchange "DTI' for credit utilization. I believe OP is trying to bring mortgage scores up.
I agree with the great advice everyone gave you as you are way too close to closing time.
Personally I did exactly what you want to do. I applied for an Amex and a chase freedom unlimited right after getting approval to start my build, so I had 6 months to recover. I gained an additional 36k in available credit and my score eventually went from 680 mid mortgage to a 725 mid mortgage. I spoke to my loan officer whom I asked to check with her underwriter to be sure it would not create an issue as I only wanted to improve scoring and move from FHA to conventional. I would add that they are aware of my plans to cancel all my junk credit cards after closing.
if I can I would strongly suggest you check the credit card forums and research soft pull CLI credit cards to determine if you have credit cards that you increase to further reduce your DTI. If it's possible you may be able to squeeze some added points. Add that to paying down your current debt, you'll be in great shape!
Best of luck!
I would definitely not do this, no offense to the poster of this, but this could still look like a risky pattern to your mortgage lender, there is no harm in waiting till you close. The offers will still be there when you do!