H1b transfer are very much scrutinized these days. Especially if u are a consultant. And even more, if your degree does not match your job. I don't think it has been this bad ever. And trust me, I have seen a lot. Atleast, 5 of the consultants from my work, all from cognizant (cts) got there h1b rejected and cts immediately asked them to leave the country. And these were direct vendors. I think almost all had EE degree and they tons of years of experience. Matter of fact, cts has started processing Canadian work visa for those who would soon need extensions.
I wanna be brutally honest, your chance via consultancy is pretty much slim pickings. But do try. All the best. Also , look for others options like Canada or Australia. I was doing that last year when I was waiting for my GC. I had take IELTS and everything.