It would be helpful if you could share your motivations for moving in to consultancy and your expectations of the role and types projects you would be working on.
If you feel you've gone as far as you can in your current business and are looking for a new challenge or complete change of direction - then consulting may be the right move. Lots of different clients, different industries to try, politics, sales process, pitching to learn etc...
If you are looking to accelerate your career in your current field, it may be less appropriate. As mentioned, it sounds like you already have the kind of role that many consultants are looking to get.
In my opinion it's tough to leave consulting for a role that is more senior than a senior manager - unless it's for a specific transformation or project role. And even then, consultants often look at these as a route in to a more BAU/ line management position further down the line. (I'm not a recruiter - so recruiters feel free to correct me if you disagree?)
In short, if you're looking to try something a bit different and are OK with the travel, some long hours, more politics and self-promotion...then give consulting a go. I'm sure you'll get a role - if you meet a certain level then they're easier to get than industry roles. And you may even like it and reach the top.
If you're hoping it will accelerate your career so you can get your boss' boss' job, give you more responsibility or implement complex change programmes in your specialist area - probably give it a miss.