If you cubby-holed yourself as a firmware engineer, you are doing something wrong. Firmware works hand-in-hand with hardware. To write good firmware, you need to know the "in"s and "out"s of your hardware really well. So well that, you might have as well designed it.
If you look at it from this angle, the difference between h/w engineer and f/w engineer is already very blurry in my opinion. But if your desire is to go play with PCBs, soldering, putting discrete components together to make a circuit board, you just need to find a position which will give you this opportunity.
Having said this, as an EE with both BS and MS degrees myself, let me clue you in on something that you might be overlooking: The days of building harware with your bare hands is basically over. In the past, when I was a fresh grad out of faculty of electrical engineering, we had a chance to go to the electronics parts store, buy an 8086 CPU, some RAM chips and get a wiring board and put together a low grade computer system which actually worked. Now, go open the guts of any electronic device if you will. All you see is two or three surface mounted components, doing everything under the sun. Unless you are the FPGA and/or ASIC designer, under the name of hardware design, you are basically doing nothing as a hardware engineer but rearranging what someone else had developed. And when you talk of chip design, you are again talking about a very low level firmware design, unless you are really into silicon dicing and fabrication process engineering.
Yes, there still are power systems, which use discrete components to build, but everything going low power nowadays, the glory days of power systems engineering is not too long in my opinion.
So, in short, you can do what you want, but your area of work is shrinking with every passing day. Leaving your current careerpath and going h/w engineering route, is a little risky for job security, if you ask me.
My 2 cents.
