How do I transfer/save/keep data,documents,notes etc from icloud to my iphone?

Question

Ok, so here's the deal. In my old iphone I was using an apple id (let's call this one X) for icloud, and my notes, "pages" documents etc were being stored there.
However, I recently bought a new iphone and had to stop using this icloud id (long story, no need to analyze) and create another one (let's call this one Y). So I'm still using apple id X for everything else (itunes, app store etc) but for icloud I use apple id Y.
The problem that occurs is that everything that was stored to icloud when I was using apple id X cannot be transferred neither to my device permanently and be kept there (I would be just fine with that) or transferred to my apple id Y (I actually have no idea how to do this. So I kinda bet my money on the first option).
This is what I tried:
I logged into icloud using my X id and the devide started downloading my notes and pages etc. Then I chose to delete the icloud account (in order to log back in afterwards using my Y id). First it warned me that if I deleted the account I would lose all the data from my phone that had been stored in icloud. But the next message was asking me If I wanted to keep the data. A little paradox here. Anyway, of course I chose to keep the data on the phone. However it didn't work. Being at the stage with "no icloud", all I was left with, were the data I had created and stored on my new iphone. Nothing was kept from icloud X. The next step was to log back into icloud using the Y id and the data that were stored there appeared as one would expect. But of course no sign of the data from the "X account".
So, is it possible for me to somehow transfer or save or keep  in my iphone, all the data that is stored in icloud under id X, and then start using my apple id Y for icloud without losing nothing at all???
Is icloud a bit of a one-way path or is it just me?
P.S. I often log into both icloud accounts from my pc to check them and everything is still there and is intact, so fortunately I haven't managed to mess up anything (yet).

Answer 1

Thanks for your reply but maybe it would be helpful if you could elaborate a bit on that or maybe I was not clear enough in my question. What I need to do is NOT stop using icloud. But gather everything that is already stored in my old icloud account (X) and save it in my device (iphone, ipad etc) and then continue using icloud but with my new account (Y).
In a scheme:
"->" = "becomes"
Step 1) data from X -> independent device data, and then the X account is removed from the device while the data stays.
Step 2) account Y is added to the device.
Step 2 continued) now the device has a. "the independent device data" that was drawn from the account X and b. the litte piece of data from Y that I have already created.
Step 3) independent device data -> data in account Y (along with everything that is created from now on, and everything that has been stored there. The little piece mentioned above.) Everything should now be merged in Y. Merged in a "good" way. Not overwritten, not deleted etc. Nothing should be lost (old or new, from the device or from X or from Y).
The last step is kind of optional. If the best I can get is having data associated to Y (future and past) AND "independent device data" that is so independent to the point that it cannot be added to my Y account since icloud recognizes and stores only data that is created after the account's addition to the device, then I can deal with that.
I hope I cleared everything out.
I need my notes and pages documents from my old icloud account to become independent device data and just stick to the device. And then, if possible, be uploaded to my new icloud account.