Hi kittykats,
I also have dysautonomia so I know exactly where you are coming from!
First off if the reason for switching is to control bleeding, this is not a particularly good reason as bleeding is more likely with oral.
Less of it is absorbed, and most of that is converted into other metabolites, which MAY cause dizziness and sedation - however this is not a given, and if you took it at night when you had no early morning commitments the next day at the lowest available dose, you could test this out.
Unlike many medicines, taking progesterone on an empty stomach REDUCES the amount absorbed, so you could do this as well.
If bleeding is the main issue though, especially if progesterone presents tolerability issues - I don't tolerate my own progesterone well, so am on back to back COCP to prevent ovulation - I would recommend looking into other non-diuretic progestins like desogestrel 150mcg daily for example.
I don't know about you but I would never have an IUS because of the increased risk of a severe vasovagal response - you may get clinicians unfamiliar with dysautonomia suggesting this.