If you gestalt a Monk with a UAS variant Swordsage, do their Unarmed Strike progressions stack? If so, what would be the damage out put be at 20th level, assuming INa, other such feats and Greater Mighty Wallop bonuses?
Gestalts don't allow double progression of the same thing so you would have to take a regular swordsage.
As for bonuses that can really depends on your race. Greater Mighty Wallop adds up to four sizes for 20 hours(bludgeoning only), the fang ring also acts like INA without actually being it. As for the race shifters have size damage increasing badness. As a shifter you get to choose one out of like ten shifting abilities which give various sorts of nature oriented bonuses(natural attacks, senses, different terrain speeds..etc). If you choose either the razorclaw or longtooth forms and are raging while using there is the feat called Shifter Savagery that increases the damage of your natural attacks by two categories(note the language doesn't say anything only having to be the ones from the shifting). They also have druid substitution levels that do the same thing instead of wild shape as well as increase shifting ability and can add a semi-permanent +6 to any physical score. If you want a gestalt capable of unleashing natural attack badness shifter barbarian/druid with the described feat and beast strike.
"if the two classes you choose have aspects that overlap (such as Hit Dice, attack progression, saves, and class features common to more than one class), you choose the better aspect. The gestalt character retains all aspects that don’t overlap."
Now, I don't doubt that there are a veriety of Gestalt builds that COULD bring damage modifiers from both sides that are different and would synergize well. This is not my area of expertise, but no doubt others can offer suggestions.