There are several open access solutions but few (if any?) open source solutions. Arxiv is free but lacks reputation outside a small number of fields. PLOS One has a decent reputation in some fields and probably comes closest in being good value.

I know a couple of people working in this space, and ultimately it ends up being a networking issue: in order to get peer reviewers at a scale which is acceptable, you basically have to buy editors with networks of contacts. Since good or even mediocre reviewers are scarce, this ends up leading to significant competition for reviews. But reviewers are not compensated so there is no market pressure for reviewers to actually exist. Publishing is now a profit-driven system built on top of an informal network created by enthusiasts who were originally doing the work because it was important to them.

There have been a couple of attempts at matchmaking systems and rewards systems. https://www.reviewcommons.org/ is the most visible in my field, but they only get 1-2 preprint reviews out per day so far. This is still quite new and there are a couple of other platforms in development.