Do you actually have any symptoms or issues with your bowels, upper GI tract etc? Anything disrupting your life, nauesa, vomiting, pain etc? If not then I'd leave that, watch it but other than removing them, there's not exactly anything to be done. If you did have a hysterectomy you could talk about perhaps getting general surgery to remove them but it can be complicated etc, if they say its medically unnecessary.
I'd wait on the coil etc, it can take up to 9 months, but for most will settle before the 6 month mark. Whilst it's settling I'd ask for some northisterone to use for periods. For your pain, perhaps try another NSAID, or the same one with a higher dose, make sure you take it consistently, a few days before the pain starts, with food and omeprazole as well.
Then if it really isn't working it's either ablation which is an amazing option for many with bleeding etc, and somewhat for pain or a hysterectomy.
Have you actually gotten an appointment with a doctor in the gyne department this week? As otherwise over the phone or just asking, they won't have time, with outpatients, doing surgery, on-call with inpatients. The best you could likely do is speak to the secretary and get an outpatient appointment booked in - I'd get it for 5-7ish months time because you want to see how the coil is going, if you have it too soon, they may 1. Discharge you from their service and say get a new GP referral if it fails or 2. Say that it's too early to tell and not book anything in.
You could also ask the secretary if you can have a call with one of the endo nurses as they tend to know lots about adenomyosis as well and would be more likely to get that unscheduled.
Also ask the secretary about waiting times for letters and surgical reports, they can be quite long, ask about the earliest you/your GP can get them, so you have a timeliness for seeing them on the app etc. Also ask how many surgeons were involved in the surgery, you could ask endo nurse if she knows if there was any other surgeons and if so if they thought differently or the same etc.
If you do manage to talk to a registrar or consultant or nurse, I'd ask about if you do go down the hysterectomy route, whether they think a total one with removal of ovaries or cervix is a good idea or not. If so, think about HRT etc and surgical menopause which can be a lot. If you do go down that route, I'd lean towards just removal of uterus but it's up to you.
Definitely see your GP though and make a plan, then check in via econsult or online form when the reports from surgery get sent to GP.