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The best advice I can give you to say that yes, sciatica and piriformis are absolutely TMS. After truly believing that you have TMS and knowing other people have recovered from what you are experiencing just stop thinking about anything related any other name (piriformis) for your TMS. Comparing your specific pain sensations to other people's pain is a distraction that perpetuates your pain. TMS is TMS and most of us will actually have many forms of TMS throughout our lives because we are human. Because of that my advice is general because there is nothing special about piriformis syndrome or how to approach it.
Here is what worked for me. It was not a straight line, it didn't work right away. But now days I can sit without pain for hours without pain. I can eat wheat bread without pain.
1: Believe you have TMS. Believe there is no physical cure, believe you are actually physically healthy. Your brain will latch onto any doubts and create pain that supports the experience of a physical problem. Knowing doesn't help, believing helps.
2: STOP ALL PHYSICAL CURES: no more avoiding positions or activities, do them anyway. No more special pillows for sitting or wearing just the right supportive shoes. No stretches, no massage, no chiropractor NOTHING. Any time or effort you put into those things prolongs the pain.
3: THINK Psychological. For many people that involves some kind of journaling, there are many many resources for that. There are programs on here, there are many books, look up anything by Nicole Saches. I found Alan Gordon's resources here in TMSwiki to be the key for me. Initially I would remind myself of this all day long and talk to my pain "I feel you there, you are actually my emotions that I'm feeling in my body."
4: Become indifferent to the pain. OK now this is really hard and it is absolutely what worked for me. Search anything related to "outcome independence" on here. Basically the next step in my conversation with the pain was "I feel you there and you stay as long as you like, actually get worse if you need to." For everything else I had tried it had never occured to me to accept the pain until I was reading some of the info on here from Alan Gordon. And if you cannot imagine giving your pain permission to stay and get worse PRETEND YOU CAN and say it anyway. There is magic there. The first time I invited the pain to "bring it on" it was GONE within a minute. It came back on and off for a couple more weeks because that is where my neural pathways were wired back then, but I'd just welcome the pain again and again and it would fade away. This is a skill. This is weird.

To answer your question about timeline. From finding out about Sarno/TMS to being free from chronic pain was about a year.
Here was my experience which isn't the same timeline as anybody else's because it takes as long as it takes.
Step one BELIEVE: happened in January 2016
Step two STOP PHYSICAL CURES: about July 2016 (those were hard hard times when I knew about TMS but didn't understand how to approach it and kept returning over and over to the hope of a physical cure)
Step three THINK PSYCHOLOGICAL : August-Sept 2016 (still in pain). I had NO IDEA how much stuff I wasn't allowing myself to feel or admit to myself because those feelings are "bad."
Step four INDIFFERENCE TO PAIN: late Sept 2016. No pain: by the end of October 2016.
I feel like I was very fortunate. It takes as long as it takes.