There are no published rules for this.
There are no published rules for doing exactly as you describe. But all is not lost, with some communication, you may be able to work with your DM to reach a favorable outcome.
Adamantine Plate is far more valuable than other Adamantine armors - ask for a trade.
While it is not explicitly stated, the value of an adamantine armor piece is "value of the armor + 500 gp". See here for some analysis: What would be the price of Adamantine Plate armor? Using this method, an admantine chain shirt would have a value of 550 gp - singificantly less than 2000 gp, and it does not give disadvantage on Dexterity (Stealth) checks.
Now here's how I dealt with a similar problem.
Be me, warforged paladin.
Party was just awarded five, yes five, mithral chain shirts from the castle armory.
There's a problem with mithral chainshirts: chain shirts already don't impose disadvantage on stealth. So the mithral feature of a mithral chain shirt is largely useless. No one else in the party had use of a chain shirt either, so we asked the DM if we could trade them for a mithral plate. We did this across two conversations, one out of game, one in character. First, I approached the DM out of game:
Thomas: Hey DM, we don't really have any use for all these chain shirts, what do you think about making arrangement in game with a local smith to work them into a mithral plate?
DM: I see. Yeah, I'm sure you could arrange something with a local smith, let's play it out in character and see what happens.
At the next opportunity, the party patronized the local blacksmith, and were able to arrange to have the chain shirt fashioned into a lovely mithral plate, after some in character haggling. We gave the smith all five chain shirts, and let him keep any remaining materials after the plate was finished.
The out of game conversation was longer than this, but the idea is that the party communicated with the DM that we didn't actually have any use for this in game reward, but we wanted to do something more interesting than just sell the pieces. Obviously, you want to avoid framing this conversation as "hey DM your loot sucks give us stuff we can use" - frame it as "hey DM let's work this cool loot into something we can use, since that's way cooler than just cashing out". So for you, I suggest having a similar conversation with your DM, asking if you can work the adamant plate into chain shirt, so that you can benefit from the adamantine feature and your natural armor, without having disadvantage in Dexterity (Stealth) checks.