Your printer does not have something called a Prime function. But something similar to that is in the head cleaning menu. Basically if your first head clean operation is not sufficient, you can choose to do a second cleaning, and that MAY use MORE ink to flush the head.
I just noticed you post about the BCH cleaning solution kit and watched its YouTube video. That is similar, but maybe a bit better. The fittings to force the solution through the head are better. I do NOTE that the procedure recommended is different. Instead of flushing in on shot, they simply try to fill each colour of the head with a smaller amount and let it soak overnight before proceeding. Then they do NOT force more cleaner through. Instead they re-install the ink cartridges and use a normal Head Clean step from the menu to push ink through. If this is moderately successful they do an extra Head Clean, maybe two. They appear to suggest that the entire process could be redone only if the first time around is NOT completely successful. All of that sound like a good process to me.
So, if you "new" print head still is giving trouble, you could try the BCH product and process on it BEFORE doing many normal Head Cleans, since they use up a lot of ink and may NOT do the job. I believe you already have tried that.