Sounds like you have a good grasp of the benefits you bring yourself. If you're personable and have self-confidence you should be a sure thing if you get through the recruitment consultants to a technical interview. Have confidence to sell yourself on that generalist, adaptable, not just flavour of the month, problem solving track record. Particularly emphasise how you have handled responsibility and shown leadership. Don't sell yourself short so that an existing technical manager doesn't feel undermined, if you're selling yourself up you don't need someone putting you in your place you need somewhere you can take on responsibility and build your role. Take your skills elsewhere.
I think you sound like a technical leader any sensible organisation should hire over a niche greenhorn. Whilst HR types might be averse to someone with less pigeonholed skills, many mature organisations need adaptable problems solvers who can fix problems more than someone who knows the latest J* golden hammer and can be hired by the day from Tech Mahindra. If you've worked on large projects before, emphasise what you achieved rather than the means you used. Even in companies doing swathes of outsourcing they'll need generalists who can spot bullshit and quality control the outsourced development teams / cloud services. Non-technical managers just can't do that. Project management can be a separate stream in itself where you're competing with folk who've done Prince & that kind of right of passage management specialist stuff so not a shoe in, but having a solid technical skill base would put you in a different class for project or techical leadership essentially as you can't be bullshitted. Moving up to running a technical team or being a technical director in a small company would seem a good move. If recruitment consultants are getting in the way find better ones, use your contacts or contact employers directly and pitch yourself as a highly skilled senior technical leader with a track record solving problems on serious projects, ex of your most impressive employer rather than underselling yourself by competing as a narrow pigeonhold DB/Java/support specialist.