I have recently had a reply from an owner of a Persian cooking site who told me this:
"Making a successful tahdig in a stainless steel pot is very tricky. Although not impossible. However, I wouldn't recommend it. Not only is it hard to turn out a good tahdig, but can damage your pot, as well.
I like to use a well seasoned cast iron pan, or a non-stick pot. I also make rice and tahdig in my cast enamel Dutch oven style pots, like Le Creuset. But, cast enamel can be temperamental when it comes to tahdig, too.
A couple of tips: 1- Grease the bottom well (sounds like you're already doing this). Use a combination of butter and oil. 2- Use a heat diffuser. 3- When ready to serve fill your sink with a small amount of cold water, or wet a kitchen towel, place pot in sink (or on wet towel) for about a minute. This should help with the release of the tahdig. "
Many of those on youtube also use non-stick pots. I'm just afraid of making my non-stick...stick!