A number of things are wrong with the Guy 2 answer.

First, "heat pressing" is simply the wrong fix for the Martin. The loose fitting 3/8" metal tube cold creep of the glue allows excess relief over time. Heating it and bending it back is at best temporary. It will bow again. Compression fretting is one one permanent fix, but there are others.

Second, he linked (or as stated by the OP at least) excess relief and a neck reset. Both problem affect playability, but other than that they are unrelated. I suspect Howard had that in mind when he made his comment.

The Thompson Belly reducer is a different thing entirely. It was developed for use on vintage instruments which are primarily built and repaired with hot hide glue. It does not tend to cold creep, so the fix is more permanent. It is also made correct excessive belly caused by a number of things, including abuse. Presumably the guitar will be treated better moving forward. In the OP's case, it's not poor treatment that caused the problem. The belly reducer may also be used in conjunction with re-gluing or replacing the bridge, which is a substantial brace and will also help maintain the geometry.

Regarding the bass you worked on, did it have an adjustable truss rod? If so, I'd guess you used that and heat to straighten it. The OP's Martin depends solely on the stiffness of the neck. Heat pressing does not increase stiffness, hence the temporary nature of the improvement.

Long story short, heat pressing may have some limited utility but more often than not I see repairmen suggesting it when they have no real idea how to fix the problem correctly. It's an early indicator that a different repairmen is needed - where my guitars are concerned anyway.