Birth Control and hEDS?! Help!!

Hello fellow bendy people! 👋🏼
I really hope you can help me as I feel pretty lost and confused. 😵‍💫
I have hypermobile Ehlers Danlos and have been on the combined pill for around 9 years (Lucette). I have been told by GP Lucette is quite a high risk for clots, especially after the length of time on it and because I get migraines associated with the hEDS higher risk. (I do not get auras though). Lucette has been pretty fantastic when I am on it regularly.
But on my break week I also get a lot more joint pain and migraines for 1-3 days.
It’s taken a while to find a GP that understands the correlation between EDS and hormones. So many I saw kept advising the progesterone only pill as the safest standard switch 🙄 (how many times did I have to do their job for them and explain progesterone can make your joints looser?! I lost count!)
A lovely GP is going to try and get me a gynaecology referral . But in the mean time what have your experiences been???? I would love to speak to fellow stretchy people to discover your experiences and feel a bit less confused.
(I don’t want to get pregnant but I also very much don’t want a blood clot!)
Thank you 🙏🏼