Re the Jaydess - this has been discussed in detail a few months ago - so you might like to see the thread on it here:
https://www.menopausematters.co.uk/forum/index.php/topic,33744.15.html . I did some basic comparisons with Mirena and maybe HRT products containing levonorgestrel (I didn't read the thread completely). It is licensed for contraception though so perhaps that is a starting point?
Someone on here recently asked at her practice to be prescribed this and was refused - so it might have to be a private consultation or a NHS meno clinic - perhaps phone them beforehand to see if this could be possible?
By the way your consultant is quite wrong to say that it is not systemic - as I may have mentioned on that thread - it is only relatively non systemic by comparison with birth control pills that contain the same progestogen, and which are taken orally in large doses. I did work out that the Mirena at some point during its life would give rise to systemic levels of levonorgestrel of roughly the same order of magnitude as the Femseven HRT patch.
I agree you should not need a biopsy unless a US and TV scan have showed thickened endometrium and possible irregularities or you have had abnormal bleeding - however different gynaes may have different approaches?
If you have been skipping the utro and don't have a cycle of your own ie are post-meno then your lining is likely to have built up and therefore at some point you are likely to bleed as it sheds - even with continuous progestogen from eg the coil.
I presume your degree is almost finished as exams are usually over by the end of May/early June - so at least hopefully you can get back on track with the right HRT?
Hurdity x