It sounds to me like you have too much sand on the arena.
Three inches of sand–although that’s what footing resources often recommend–is too much. I would recommend to put down 1 1/2" inches of sand in an outdoor arena to start and then add more as needed, because it is so incredibly easy to end up with too much. In your instance, the best thing to do would be to pull off sand. It costs $$, but arenas are a pain in the rear and you are not–by far-- the first person this has happened to.
Sand is typically measured and loaded by weight, not by volume. So if the sand you purchase is dry at the time (or dryer than normal) you are going to end up with more sand. If you try to do the calculations of converting the calculated volume of sand you need into the weight of sand you need to purchase, it’s quite tricky and easy to err on either side.
Regarding round sand (river sand) vs angular sand (mined sand), yes, angular sand is more optimal for horse arenas. It “rolls” less underneath the horses’ hooves. However, depending on the area of the country, many people use river sand for horse arenas. Watering (or a footing additive that holds water) can add grip. Also, some people add crumb rubber to river sand, which also adds grip. In the olden days, people used to add clay to the sand and then water it, but clay adds a lot of dust when dry, and I wouldn’t recommend doing that.
If I were in your shoes I would pull off a decent amount of the sand and then ride on the arena and see how the depth is. Hold the extra sand in reserve and you can always add it back. Alternatively, if you feel that the sand is rolling too much, you could consider adding crumb rubber to the sand.
I would not bother with trying to replace the sand with an angular sand, at least not at this point. I think you need to start with removing sand first and then see where you are.