My Galaxy S4 is of the model SCH-I545, which is not largely supported for rooting, Ubuntu Touch, etc. Would it be possible to change my phone to a new model by installing other S4 firmware, or something of that sort?
Probably not. While the models are close, they have hardware differences which make using the proper root method/rom critical. You might be able to trick an app into thinking it's installed on a different model, but you can't trick the hardware into changing to something it's not. Sorry.