Is there any sort of reverse head hunter service? (A service where a person finds suitable employment for you and maybe makes introductions)?

You are not looking for an employment agency. Employment agencies and headhunters know of jobs and try to find candidates that fit those requirements.

You are looking for career counseling services. These are individuals that will help you with all different types of job search skills from resume writing, networking, interviewing skills etc. There is a fee involved in this.

Or if you are an university alumni, your university's career center can provide some of these skills but not as specialized service.

A lot of HR professionals put up their signs and say they do this but they don't. You need to find individuals who have been in business for 10+ years. Most work directly with employers during downsizing, but will take on few individuals.

That;s what employment agencies do

They are called employment agencies. They have different contracts, so read them. The servvices and percentages differ, and whether you can break your contract and get a job somewhere else without paying them is a key issue... Say they do a terrible job, but YOU find a job on your own sometime in the year that is covered by the contract... You can end up having to pay them a percentage of your annual salary the first year you work at this job you found on your own.

There are also professional resume writing services, if you think that is the only problem, or employment coaches if you think it may also have something to do with the way you dress or present yourself.

Sadly, gaining employment does not take the same skills as keeping your job, or doing a good job... It has a lot to do with sales (of your self, as well as your services), keeping one has a lot to do with getting along with people, neither of these has much to do with your qualifications to actually do the work.