As mentioned before- don't use anything to increase the pH, your betta will adjust to it just fine, and playing with it can easily cause harm and even death to your fish.
He needs more water changes, definitely. Like, 3-4x 50% per week -minimum- changes in a tank that size. That's why his fins are degrading, high ammonia exposure makes fish prone to fin rot. It'll be ammonia from lack of adequate water changing, and not the ph, that's affecting his fins.
(I'd make the water changes after removing the stones, etc, quite small and frequent over a few days, to help the fish get used to to the new water chemistry)
With a live plant, you don't want to be doing so many water changes.. and not that many in a 1g with no live plants either.
Your tank can become too sterile, which in the long run will cause your fish to have a lowered immune system since they won't be exposed to everything a healthy fish should be exposed to.. among other reasons (not at home, so don't have all my files).
The plant needs the waste and to have the organisms in it to live healthy, so do the shrimp. Personally, even though shrimp give off little ammonia a 1g is quite small for them- the shrimp may not live as long, nor be as healthy in time because they do require a larger tank, and one that has some sort of cycle.
Have no ideal why you are using AQ salt, in fact, surprised your shrimp haven't died from it yet.. if it is just a torn fin, AQ salt can actually hamper the growth of it. Stop AQ salt right away unless he has an open wound, fungus or a bacteria infection such as fin rot- if that is the case you should remove the plants and shrimp, 1tsp of AQ salt, daily 100% water changes for no longer then 10 days. But if you aren't treating for any of what I had listed, then it is best to stop AQ salt, do a 100% to remove it and then start on the proper water change routine that is specific for your set up:
2 50% water changes a week, that is all. You can remove some of the waste with a turkey baster once a week or every other week (your plant will use the waste as fertilizer, so you don't want to remove it every time).
As long as you do suck up some of the waste as mentioned just now, then you can eliminate the need for a 100% because you have a live plant in the 1 gallon.. that plant is keeping your water cleaner and safer then if you didn't have it. People keep forgetting that bettas don't create a whole lot of ammonia themselves.
Again, don't mess with the pH, don't go crazy on the water changes, recommend to rehome the shrimp... have to keep in mind that every tank is different, and the water changes isn't cookie cutter same for every size tank. There is the basics and recommendated amount- but have to keep in mind if people have live plants and other animals in the tanks that it won't be the same as the next.
And regardless you don't want to over clean the tanks anyways... a 1 gallon unfiltered tank should be cleaned no more then 1 50% and 1 100% per week.. that is a tank with no live plants, no filter.