This is my experience so it may or may not be the same for you. I have a 90 day notice period in my company too. So I got literally 0 callbacks even after applying to over 1000+ jobs.
3 months back my company gave me a bench letter because I was on bench for a long time. So they told me to find a new project within my company in 3 months (which is my notice period) or find a new job outside.
It came as a wakeup call for me.
I started applying again , this time more seriously.
When I had 3 months left - no callbacks
2 months left - no callbacks
1 month left - 1% callback rate but I couldn't crack any interviews
15 days left - I got interview calls by 15 different companies
So what I'm trying to say is having a short notice period really helps.
BUT
it depends on how good you are because if you quit without an offer and you don't get placed in a new company that'll be really scary