(I am not ...criticizing you, but there are some problems, specially between the real world and ...movie/fantasy world) But you are getting close and aren't far off.
why a heavy 76 mm, when you can do the same ting with a lighter 56 mm gun or a even lighter 40 mm gun with smart ammunition.
In may experience of modern ships, I see two 76 mm guns normally on a ship like a frigate or bigger, that will say a ship that weight more than 3000 tons. Remember that the Type 130 is around 800 tons Heavier than you'r ship and 10-15 meter longer and at the same time is lighter armed than you'rs
you'r ship will weight around 1000-1200+tons
you have a Heavy radar placed high up, you have two heavy 76mm guns, and you have more Harpoon than any ship of this seize naturally have (except in some circumstances, but those ships dosent carry anything bigger than a single 40-56 mm gun)
You have to remember that you want the center of gravity as low as possible, now you have a lot of heavy equipment high up, that push you'r center of gravity up high, making the ship unstable, and it will just capsize by just looking at a wave.
all you need for your role is:
- 56 mm gun on the forward deck, it handle both the land attack role and air defense duty. (The Norwegian Skjold can carry the 76 mm on a smaller hull, because it's an Surface effect ship SES, it's a catemaran and hovercraft in one and same ship, but if you see video of it, patrolling in waves, you can see it always moving on it's bow, due to the weight of the gun)
- two quad pack Harpoon canister, mounted at an 45 degree angle (they take up quit a lot of space, and need free exhaust.
- 2*12.7 mm guns that are remote controlled
And if you need artillery support during a landing, you are going to bring bigger ships. And anyway for long range artillery support you are going to use missile, like Tomahawk or NSM/JSM with land attack capability, short range are almost direct fire, and many of the 56 mm ammunition works perfect for that role.
Ships have limits to what they can carry