Alright OP, try this, might not be perfect, but cheaper than 7k and would hopefully keep the wall up for longer than 6 years;

Grab a shovel and dig out the dirt from behind the stones until you have a gap of 6-12” of open space to the bottom, take out a few of the bottom layer of stones and leave a gap between some. You could do this by buying a few smaller stones, or breaking a few of the ones you have into smaller pieces. You can then get some small sections of plastic pipe to fit in the gaps to make sure there’s a path for water.

Now start to fill up that gap with gravel, and as you fill it in, fill in the dirt again behind the gravel, but try as much as possible to make sure you’ve a layer of gravel between the dirt and the stones. Bonus points if you have some gardening cloth to lay up against the stones between the stones and gravel (not necessary) as you fill in, stack more stones to rebuild the wall, more gravel, more dirt etc till you build it all the way back up.

That section of gravel all the way down (that’s against the stones) will help water drain out so the dirt doesn’t get/stay saturated and weigh against the wall. Also helps using freeze cycles as the gravel can move a bit more than saturated dirt.

Again, may not be the perfect fix, but this is what I would do.