Other possible solutions whilst waiting for the mirena are taking it vaginally - some women get less side effects this way, or taking 100mg every night instead of none for 2 weeks then 200mg for 2 weeks.
Yes you might get some irregular bleeding with continuous use but it may be a price worth paying if you feel less wretched on a lower daily dose. (Remember there's no medical reason for induced withdrawal bleeds, these are simply built in due to paternalistic beliefs about what bleeding pattern a woman should have, and endometrial protection is superior with continuous progestogen).
If you could be waiting months, some GPs will sanction off label use of 150mcg desogestrel as the progestogen. This would mean taking a double dose of Cerazette or equivalent.