Your physical condition made it harder to achieve success, but sounds like you are on the right track anyway When doing SILD, remember it is not necessary to stay completely motionless. You should feel as comfortable as possible, as long as you don’t fall asleep before finishing the cycles. Stopping “intentionally” in middle of it is actually okay though.
It is perfectly fine to move somewhat during the exercise, swallowing included. In fact, at step 3c, where one scans for body sensations, one may do it so aggressively to the point she actually moves the physical body. While this is not encouraged as you may lose sleep, it is indeed fine and works equally well.
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Yes you should do whatever to fall asleep quickly. For me that means completely throw away everything and just DO it, but people may differ. No need to chant mantras and telling yourself you will be LDing later. That job has been done by the cycles. Just go to sleep, as quickly as possible. The quicker you can fall asleep, the easier it is for this to work. If you do plenty of repetitions and fall asleep quickly enough, chances are you will experience the strange sensation which you wake up suddenly into a trance with a very clear and alert mind. It feels like miracle.