My name's Kel.
Need some more information --
Where are you located?
When was your home built?
When you say sinking bad -- how far have they sunk?
Is the rest of your home stable -- that is -- it's not sinking?
Is the water table abnormally high?
Do you know what kind of soil the home is built on?
You mentioned gravel -- was that added or is that what much of the soil is comprised?
This kind of problem is not usually covered by homeowner's insurance. That usually protects you from disasters like a tree falling on the place. Most policies nowadays exclude rot.
Can't think of a simple inexpensive way to repair.
I'm based in Minneapolis. The City provides loans to people to fix their homes. If they agree to stay in them for ten years and not turn them into rentals the loans become grants and are then forgiven. Do you have any programs like that in Ontario?
The most efficient way to remedy is to remove the floor, install piers and beams and rebuild the entire floor.
Given your situation what I'd recommend is triage. Start with the worst spaces that are most bothersome and repair one at a time. The kitchen would be the place to start. The kitchen appliances and cabinets will have to be removed. Pier footings will have to be excavated and installed. Beams run from the existing foundation to the piers. New floors framed and decked. Then the kitchen reinstalled.
You're rebuilding the floor piece by piece.
Next I'd do the bath. Then the bedroom then the hall.
Wish I had some magic for you.
Have I answered your question?
Discussing addition plans would be beyond the scope of this question.
Doing an addition and then renovating the old section would be an excellent strategy if you can make the money work.
The International Building Code has 7'-6" as a minimum ceiling height for habitable rooms. To get a better quality space after you remove the rotted floor either in its entirety or section by section as I suggested you could excavate down a foot or two then rebuild. It's more expensive, but the home would be much more appealing and valuable.
In order to have adequate headroom and a floor thick enough to be properly insulated you can either remove the ceiling or go down. I'm guessing it'll be less expensive to remove some soil where the rotted floor is currently resting.
By lowering the soil level when you rebuild the floor you can have higher ceilings.
It would certainly be possible to have three steps between the new addition and the old section of the home.
I'd recommend meeting with three renovation contractors to get ideas and rough estimates on how much it'll cost to do the work.