“I bought from many different suppliers (from what they say, all top quality)” Most of the batteries being sold in the market for iPhones are used or low quality. Batteries stay inside the phone, so a used battery or a new battery will look the same, there’s companies that receive the original used batteries, put them in a new plastic pouch and sell them as “New Original Replacement Batteries” in the market. There’s also batteries that although are new and have the same outside looks as the original Batteries are made to really low standards. The goal here is to achieve the same outside looks (pretty simple) and make it just able to hold a charge (even if only lasts a few minutes), while skiping and saving every cent in all the raw materials used. AVOID ebay and aliexpress battery offers and sellers. I don’t have experience with iFixit batteries, it would be nice to see some tests comparing to an original one.
Should I decide to do it - would it help the machine run cooler if I milled or drilled some holes on both sides of the bottom case? Yes, of course, you just need to do it in the right places. Be aware that most images on the WEB showing drilled Macbooks have the holes in the wrong place because people didn’t understand that the Macbook fan in Centrifugal and didn’t study the Macbook Airflow. Macbook Pro 13 (2011) - Airflow (1) Best place to drill air intake holes is on the Blue Arrows. Or Blue+Yellow