I’d like to note that the hot sketch is not valuable in all situations.
I have seen that when NPD is done in-house, there is very little reason to spend the time on a sketch that takes more than 5 minutes to complete. Getting prototypes into the hands of the users is much more valuable for evaluation of an idea than a drawing. Interaction will always trump imagining interaction.
There is a fit for you in NPD, no doubt. My guess is a consultancy would want to pigeon-hole you into the shop. Corporate NPD would view you in a better light. Your best bet is to find a fit with your current skill set to get a foot in the door (don’t try, for example, a cut and sew manufacturer as they need little machining).