I'd echo the view of Tom1, don't ever rely on just one channel to deliver. Just a few examples and insights that I hope will be helpful:
- Consulting firms have been building up their internal recruiting teams to approach candidates directly via social media (especially, but not exclusively on LinkedIn). Recruiters tell me they make most of their hires on LinkedIn this way (not via the LinkedIn jobs board contrary to what you might think). So if you haven't polished your profile and invested time in ensuring you'll show up in searches being conducted by recruiters then you're missing out on tons of opportunities.
- Plenty of hiring is happening below the radar - consulting firms needing to make hires but needing to do so discreetly / out of sight of clients. These roles usually go via recruitment agencies, so if you've discounted working with recruitment agencies then you're missing out on a portion of all the opportunities in our sector.
- Referral hiring is extremely popular with employers, as it's shown to produce some of their best hires (in terms of people who are culturally right for the firm and go on to become a success within the business). So you should be working your contacts to see what opportunities you could be referred into.
- Job boards remain one of the lowest cost routes for making hires (all the above come at a considerable cost per hire), so there's still appetite to make as many hires as possible via this route.
Hope this is helpful. To the original poster, there are a couple of recruitment firms who operate in the strategy consulting to industry space (think top MBA or McKinsey moving into a corporate role); but asides from that there's no-one I could point you to who specialises in this area - there's a wide range of firms hiring for roles in industry, but most of these roles would accept applications from more than just ex-consultants and so there isn't really a market to specialise in this.
Founder, http://www.Top-Consultant.com and http://www.Social-Hire.com