I'll say something similar to the last poster in terms of idiosyncraticity - some firms or line managers want heavy maths, others want a client facing math person etc etc. By no means a comprehensive list. Also if there is anything properly relevant in your PhD work ie actually would be useful to a practising quant, then explain why. If you're going to do that make sure it's accurate - if you do something like the quant equivalent of saying you have "project management experience" based on once putting shelves up then you will be found out and piss people off.
In terms of preparation - quant interviews are the worst and can take a bit to prepare for. Bear in mind though what interviewers are looking for is how you think. And you have been getting to final rounds - it's a myth-ish that if you were selected for first round then there is something about you - really it means you can write a good CV/resume, getting to the final round means you have a serious chance. You can consider internships, can't be any harm but also look at how to widen the search - hedge funds for instance.
There's also considering similar coding roles, data etc. I'm in healthcare at the moment and there is far more scope for moving in differnt directions while in finance there was none of that - you might be lucky and get stability, it's not impossible in finance especially in middle office.
Last thing I would say about nerves is to be pretty uncompromising about any external forces eg are family or partner pushing you around over not having a job yet? Because if they are it only gets worse from here on. The trick is detach yourself from their crap - in psychological terminology break codependency and don't try to please them or reason with them. Family members of mine have bludgeoned crass and innacurate career advice down my throat that would have cost me big time and it didn't stop until I stopped justifying and defending myself and detached family from my life. I still have to live with clowns in my family that think I never used my masters - and they're not just referring to them not realising that I use the same processes in my data work, I've heard these special cases actually tell me to my face that I didn't use a masters in financial maths in my role as a quant. Not one word of a joke.
If that doesn't apply - granted the level of toxicity in my family was off the charts, then I would just remember that if you can show how you think and that you have common sense (eg if you're asked about downturns in share prices don't say "ooohh that's interesting volatility" because you will be working with traders that are on edge. Instead describe it as a challenge that you want to smash) then you are doing well. Also most people I know that have hired people despise this HR crap around nerves - a common theme is that if they prompt you they will get the best candidates and if a firm refuses to do this then you're better off not working there. Even the senior managers in my current place, who aren't necessarily technical, find nerves hit them and I've gotten supposed "top" jobs, whatever the fuck that means, having been nervous in interview. Maybe instead think "Do I want to work for this lot?" instead of being desperate or find, say, a data entry job for the time being if you're worried about money.
