That's commendable that you want to contribute work to Github to show your stuff. But what you should really do to gain a good internship or job in general is network with those who can hire you or work at a company that can recommend you to a hiring manager. That will increase your chances much more than only applying with so many other applicants.
Should I apply to Junior Developer jobs despite being in my penultimate year of my Software Engineering studies?
You can, but mostly it'll be of no use.
To elaborate, as it appears, you are looking for an internship role / position. You need to first understand the fact that the internship and full-time employment (including the junior positions) are not ...
I tried this and didn't have any luck
I gave this a shot, also during my 2nd year. I stuck out completely. If your university has a one year long internship program, you might give this a shot, but it probably won't make a difference.
The funding strategy for interns and the onboarding process for interns is quite different from that used for junior ...