Back in the early 90's, I had no job and very few computer skills. I volunteered to work free of charge for 1 month with a computer/publishing firm. They taught me so much and hired me once the month was up.

Could you write the firms that recently interviewed you and offer to work free for a month while they assess you? It could turn out that the person they hired, doesn't work out and you're there willing and eager.

And if they don't hire you at the end of the month, ask them what you can improve upon.