How old are you? You're on continuous HRT but that doesn't really tell us if you might still be cycling and producing your own estrogen, which will cause unscheduled bleeding.
And no, the coil is not your only option.
If I were you, I would schedule a bleed. Simply stop taking the P for 3-5 nights every month. Usually a bleed will start about 48hrs after you stop it, so give it a few days to empty out. Then restart the P.
Doctors freak out about 'unscheduled' bleeding. If you schedule it so it only happens when you stop P, they won't worry. If you have any building up, eventually it is going to break through at some point. If you schedule it, you will control when that happens and let the pressure off, so to speak...
And this used to be the old 'continuous' schedule, taking it for 25 days out of 28 - so it's perfectly safe. It's just that someone (probably someone running a pharma company with a penis) decided that women didn't need to bleed and should just take it continuously. The problem with that is, if you still make any of your own, you are likely to bleed randomly and 'unscheduled' if you take continuous P - OR if you take a decent amount of E.
The other thing you can do, is to increase the P as well. I take 300mg P from day 7-14 and 400mg P from day 14-26. I am on a high E dose. I get this privately as my NHS GP probably wouldn't prescribe it without a letter from the private clinic. I stop taking P on day 26 and usually bleed by day 28-29. I start it again on day 7.
And lastly, you can also experiment with taking some P rectally rather than all vaginally. Some women absorb it better rectally than vaginally. Don't put it too far in, or it will get absorbed by the liver and have the same effects on you as taking it orally does. Just past the sphincter. This is v common way of taking it in the US.
It's really about experimenting until you've tried all options....