With a Chapter 13 your arrears and trustee payment will be something like $500 a month. I know because years ago I had about $30,000 arrears in a five year plan. Since that's out of your range you need to just ride out the Chapter 13 for awhile and then it'll be dismissed. This could take maybe two to five months. Alternately you could challenge their proof of claim and fight foreclosure in bankruptcy.
If it's dismissed or in the meantime you could look into the mediation they offer in your state. Maybe it would be possible to get a new modification with the arrears put at the end of the loan. I really have no idea what they might offer or if they'd offer anything but it's worth checking out. There are various organisations you can contact for help on this link.
You can submit a application for a new modification and if it's denied you can appeal. That will at least buy some more time. Then when they try to foreclose again you can refile for Chapter 13. I'm not sure how often you can do this because some of the law around that issue changed, used to be you could just keep on refilling.
Anyway you'll gain some time. What you do with that time it's what matters. If I were you I'd start educating myself of everything to do with your loan, the laws surrounding Connecticut foreclosure procedure, who owns your loan (you may be able to find the name of that entity on the notices you received), you should also send a Qualified Written Request (QWR) asking who owns you loan and asking for an account history, that's important, you may be able to find "mistakes" they made in which you were overcharged. If that's the case you might be able to stop a foreclosure because they are asking for money in excess of what you owe them.
All of this information could help you find out if the entity trying to foreclose actually owns your loan and had the standing to foreclose. It may also help you identify errors in filing.
Look for all the correspondence you've received on the loan (the things you were told may turn out to be useful to you) and keep it together in a note book for easy reference.
In example my servicer sent a letter saying that the investors had given them no authority to modify loans. This was an important part of my case because it demonstrated fraudulent conduct that would make foreclosure wrongful because it wasn't cured.
Use this time to learn all you can about your rights. Knowledge is the best protection against foreclosure.