You didn't mention whether you have an MBA or not, so I'll assume you haven't. The tried and trodden path for people with your background would be to get an MBA from a big name school and apply to the big name strategy firms. If you don't want to get an MBA or another postgrad degree, then you can try other lesser known consultancies but it probably wouldn't be strategy consulting.
Meanwhile, are there opportunities to become an in-house consultant where you are? A role in strategy might also give you the needed experience.
However I wouldn't leave it much longer. Conventional wisdom in consulting firms is that they don't want to hire anyone over 30 who hasn't been in consulting before. There are many reasons cited but basically the track record of age 30+ managerial types who cross over to consulting is not great.
Strategic Risk Consultant.