Andy's advice is sound, and to build on it, I'd take two disciplines in parallel:
Making yourself better at this work, and getting better at interviews.
Working through a programming project, learning new maths, and getting into the detail of various financial products are all good. As is getting some serious background reading done. This would include Nassim Taleb's books, and a variety of others about markets. Bloomberg do a variety of free courses, and university libraries have good sets of industry journals.
Also you need to learn some economics. The two big holes I see in MFE grads are in this and
C++. Many cannot even think to ask why supply and demand affects prices of derivative instruments. Purchasing power parity, rational bubbles, causes and definitions of inflation, agency theory and so much more. I'd guess 50% of MFEs are surprised at the notion of a dollar bill being a zero coupon bond.
This is not quite the same as preparing for interviews....
First up is brainteasers. A summer of hitting them hard, can more than double your chances of answering that sort of question, maybe triple or more. There's no way you can get that % improvement in your maths that quickly, if at all.
The big exchanges produce well written booklets on their products.
The goal of any sensible financial education is to teach you the
principles that enable you to understand these, which is nice but you are
hired to work on things not principles.
I actually don't know even approximately how many distinct instruments there are 1,000 ? I'll bet you've studied abut 12.
Read these booklets, at interview you can score valuable points when the trader asks
"so what do you know about STIRs ?"
In theory you ought to read up on the products handled by a desk before interview, but if you go through the HR cattle market process for newbies, you are fortunate if they are even as precise as saying "fixed income", or "equity derivatives".
You can't do them all, but every one you grok gives you a better shot at a better job.
But...
There is a deliverable in any of this, that goes beyond knowing stuff and answering questions. Managers want people with what at P&D is called "an imperative sense", and is called "enthusiasm", "intellectual curiousity", "motivation", "get up and go", or an evangelical might call "messing with things we should not know".
Managers
really like to hear candidates say "I found El-Karoui's take on change of numerarie interesting, and spent some time reading the papers on it, and trying to see how it could be used in volatility modelling".
Of course you're playing double or quits here, because for a
good job you've just said, "let's stop screwing around, ask me your hardest questions on stochastics", (in a polite way) and you emerge as either the leading candidate or are exposed as a bullshitter.
But even if you make a less challenging assertion you are demonstrating that your are not just an
educated person, but s
omeone who learns, and they are not the same thing. One is what you want for model validation, the other is who you want in algotrading or as a desk quant.
As for the summer schools, I must confess, that I do not quite see the educational value in the LSE courses that the price implies, though it does allow you to put "London School of Economics" on your resume, which is useful enough to some people that they can charge so much for it.