You are right to think that there is a correlation between previous salaries and difficulty in finding jobs. In an ideal world, if your true worth is $X/year but you're willing to work for $(0.90X)/year, then you should be able to nab a job right? After all, you're a bargain. I struggled with this myself as a student job hunting, fighting the mentality of self-worth. All my jobs previous to my new one were low pay for our industry (highest was $25/hr CAD). As someone who's had to learn to embrace this mental shift when negotiating with much better offers relative to what I was used to, the first thing I will say is that you are spot on: a race to the bottom helps no one.
So OK, let's talk about your main question: where to begin to command interviews and ultimately a better salary? The advice here so far has been standard: (a) look outside of one area (b) do side projects and (c) talk to recruiters/network. This is fine advice, but IMO, not the most helpful. Advice like "find your niche" is better... but that is a difficult task on its own, to decide on one path that is by definition obscure.
Again I will draw from personal experience to try and share what I've learned. What worked most for me was to aim for a dream job, and to do things that would lead to building skills that would make me qualified for this dream job. I was in my 3rd year of undergrad - at the time, it was to work in an NBA front office - I was studying stats, and didn't have many interests besides having fun and following basketball. In following this pursuit to its limit, I learned many skills along the way that I didn't have until I decided what I most wanted: web scraping, web development, databases, scripting, algorithm development, computational statistics, explaining statistics to non-technical users, trying to build a business, etc. Side projects, building a network (both local and out of town), and finding my niche (data science + web dev + product skills) resulted from this goal. They would have never happened on my own initiative - I would have been one of many people dreaming of app ideas and side projects to start but never finish. This has a nice benefit that comes for free: you are now different than the rest. Your perspective to solving problems and your experiences will be unique (to what degree, matters based on whatever it is you choose).
The downside of my advice is that it is not a short fix: myself, I am now 3-4 years from when I started this story, as I am soon to graduate from my MSc Stats. But you can accelerate this process, and I can tell you it works: applying to jobs coming out of my undergrad, I only heard from companies that you wouldn't recognize. This year, I got on-sites at Amazon and Capital One before deciding to accept a dream job offer at Shopify. You can do it - and I hope that this is an answer and story that can help you in your search of where to begin your change in approach.
P.S., when you get there, do not underestimate the truth behind how useful resources like CTCI, whiteboarding, etc. are for the interview stage.