I think you're worrying too much. While the heaviest burst of entry level hiring does occur at the end of the spring term, it does continue throughout the remainder of the year. Not just because there are students who graduate at the end of the summer and fall terms; but because needs for employees don't always align with the academic calendar.
A company planning to stand up a new project after the end of their Fiscal year on June 30, probably won't need to hire any junior level staff for it until at least late July. They're unlikely to have been advertising the last few months because most students would prefer not to be unemployed for a few months after graduations.
Companies that realize they hired the wrong person or who had a new hire quit will be looking over the summer and fall as well.
@Thebluefish has already addressed the possibility of applying for positions looking for a year of experience well. I don't have anything to add there.
However since you're unlikely to have a job at graduation, I would reconsider going back to where you interned and asking about a position. Not all jobs can be awesome change the world projects, and especially when you're starting out getting experience is extremely important even if you leave within a year. (Doing this repeatedly is problematic, but once or twice especially for your first job and if you previously interned there isn't going to raise any serious red flags.)
If the culture is highly dysfunctional or the business has other serious problems you might be better off staying away regardless. However "They all use IDEs, and I prefer VIM."; "I'm a Mac person and they're a Windows shop."; "They're using Java and I love the purity of functional languages"; "Subversion in 2017! Really?!?!"; or similar should not be reasons sufficient to prefer unemployment to having a less than perfect job.