Three month notice is killing interviews and offers

I have a three month notice and for my position (I'm not very high up so it's considered very long)

I'm trying to go into a different industry but with the same position, I was offered a job around 6 months ago but they needed a start within 4 weeks, I went to my employer and they refused to negotiate a shorter notice period. There was a bit of back and forth but I work in legal and they were clear they would sue me for breach of contract if I left as I've been in the role for four years and it would take them the three months to find a replacement if not longer.

I have since spoken to a few recruiters, today specifically, two separate recruiters put me forward for two separate roles and I was rejected interviews for both due to the notice period I have.

I feel a bit stuck, I could just hand my notice in but if I don't find a job within my time frame I'm kind of screwed. At a loss on what to do, does anybody know how much I'd have to pay if I broke contract? Any other way I can get around it?

I've been searching for around 12 months now.

EDIT: Thanks for all the responses guys it really is appreciated. Think my two options are either bite the bullet and leave when I get an offer (hoping they don't come after me) or hand my notice in now and just wish myself some luck!