First of all, if my approach to this is a waste of time (mine or the client's) or unethical, let me know because that's more important to me.
I'm a programmer with management, product management, and agile coaching experience. Sometimes when I'm applying to technical jobs, I see a post from a company that could, in my opinion, greatly benefit from my skills. The problem is, these job postings are for lower level full-time positions, and I want to work as a consultant. I often apply anyway, hoping that I can reach someone that realizes I can provide more value than the position offered.
Some of the times, it's HR that replies. Usually they function as a candidate filter, reading a checklist of skills and salary for the ideal candidate. If I don't check all those boxes, I don't move on to the next stage. I feel like if I could somehow reach the person with the actual problem, I'd have a chance of explaining my value (and price) beyond HR's checklist.
What techniques can I use to get past HR and reach those with the actual problems I could help with?