It sounds like you need to do some research as to what your risks in this product are, because the immediate consumer risks are not from the plastic container. For example, the phthalate plasticisers you're worried about aren't found in PET bottles, despite the name Polyethylene Terephtalate having the word in it. Think of how carbon monoxide is dangerous, but that doesn't mean that everything with the word "oxide" in it is related to it. It's just part of the nomenclature for the compound.
The products you showed are likely hot-filled acidified foods. Of note, if you are planning on canning in the US, you will also need to file a process with FDA. So again, your first step is going to be to talk to a process authority on how to make your product safely, they can also let you know of any specific issues related to the packaging that you need to address. Many sports beverages packaged in PET (such as gatorade) are also hot filled, this is an extremely common practice.
As far as heat making chemicals leach "faster". That's correct, generally when you have a chemical reaction that occurs at a certain temperature, it will happen faster at higher temperatures, but in this case for most chemicals that leach from plastic, even though there is a change it's minimal. If you imagine me pouring a gallon of water into a lake, then pouring two gallons of water into a lake. While in the second step I added twice as much water (a.k.a water entered the lake 200% faster), it still doesn't really matter as far as the volume of the ocean is concerned.
We eat food packaging every day, as knives get dull that metal ends up on the cutting board, and as we open paper bags paper dust falls onto our produce. The key is the amount and the hazards it poses.