I would very much like to use the more accurate 1-arc second data than the 3-arc second data I currently have to use, but I can't find a way to get the 1-arc second data into the .hgt format TSC uses.
Did a little bit of digging and it turns out you don't need to convert theme at all - you can get 1-arc second data in .hgt format from https://dwtkns.com/srtm30m/ . I have tested it in TSC and it works fine, and produces much better results than the 3-arc second data.