There are basically two ways to achieve this goal:
1. Gain better adherence to global metadata standards implemented at the publisher level
2. Do "annotation" over the corpus (i.e. maintain the list ourselves)
I've actually been involved in efforts on both arms of this. NISO-ALI and its implementation by Crossref provides a mechanism for publishers to provide article level metadata on license information (and embargoes). And when I was at PLOS we worked with CottageLabs to build
http://howopenisit.org/
The NISO ALI recommendations are being gradually implemented by publishers and the quality of this information is improving, if slowly. Essentially this is the same info that DOAJ aggregates with DOAJ being somewhat more complete for those small journals that only use a single license.
As you can see from the HOII website this is currently down. This was a service that scraped article pages to identify license text and collected that info. It never really got the community support it needed to build the scraper sets or move it forward to a larger scale, tho the underlying design is being used in new projects by Cottage Labs. This is much harder to do at scale than it seemed and is ultimately very fragile. Human annotation won't scale for this system in my opinion.
Overall the quality of license data in the ecosystem is improving, but its a slow process. Of course where there is actual obfuscation both methods fail. The most effective way forward IMO is to help Crossref and funders apply pressure to publishers to move faster on making good metadata available and ensure that OS platforms for publishing bake good information practice into their systems from the beginning.
Cheers
Cameron