I can't speak to your 240C - the Brother printers I have are the Inkvestment ones with the front-loading cartridges. However I do have an Epson WF-7720 with the T252 cartridges that are very similar to yours. I use refillable cartridges. You can get refillable cartridges with auto-reset chips, but I have found they are very fussy and hard to use. Sometimes the chips don't make perfect contact, and the printer complains about them, you have to pull it out, clean the contacts, and get it back in just right. And they have to be purged just right to use the first time, and hold so little ink I am constantly refilling them. I would recommend finding an Epson printer that you can get a chipless firmware mod for
before trying to us refillable cartridges with it. Or, better yet, get a Brother printer with a front-loading cartridge where the printer pumps the ink from it into an internal reservoir - like the MFC-J5845/5945/6545/6945 printers. You can put refillable cartridges in those printers and it's rock-solid stable.
It is better to plan your printer around your refill solution than to try and shoehorn a bad refill solution into an existing printer. You will save money and end up with far fewer grey hairs in the long run.