Well at least you can also upload your paper on arxive.org. But I agree, the closed journal is required for the reputation because they are peer reviewed.
(Not sure if they have some policy forbidding to disclose the paper on arxive etc. But I don't think so, the department I did my thesis, most papers were also available on arxive.org)
Most of the major publishers do now allow that kind of "self-archiving" on personal homepages and preprint repositories like arXiv. At least, IEEE, ACM, Springer, and Elsevier do, some of them as of fairly recently.
I've also self-archived some stuff that didn't formally permit it, and haven't heard a complaint. Given publishers' current political interests, I think it's pretty low-risk: I don't think publishers want the publicity that would come from suing an academic for posting a version of his own paper.
(Not sure if they have some policy forbidding to disclose the paper on arxive etc. But I don't think so, the department I did my thesis, most papers were also available on arxive.org)