Concrete retaining wall with lean and crack, looking for input
This site prefers not to provide 'call a professional' answers and I might receive some less positive reception for this answer, but this is a case where I think that it is appropriate.

My suggestion is to hire a local structural engineer to do a site visit and provide you with their opinion of the situation and additionally, if you prefer, a DIY fix solution. I say this because 1) I am a struc engineer and I have done plenty of these types of site visits and often (usually) the result that the issue or fix is NOT what the homeowner or contractor thought that it was (and changes how it is addressed) 2) the quotes you provided are large in comparison to the cost of the review by a struc and it is very likely that you would both get a solution that is less expensive to construct and you are sure that the problem is addressed permanently, you don't have to worry any more about it.

One likely outcome is that less work is required. You have noted that you addressed the water issue. Hydrostatic forces are higher than the soil forces, so more than doubles the load. These things would be considered by the engineer, and they would be on site to consider the individual situation that you have. I would expect the cost to be in a range in the middle to upper middle three digit range for the site visit and even a small change in the cost of the bids you received would more than make up for the initial cost. If nothing else, call one and ask their fee and what they would do for you. A small firm is a better choice over a large one for cost and personal service at this project level. I have no doubt that it would be some of the best money that you ever spent.