I'm not entirely sure what the situation is regarding Clinical Bioinformatics in the US - and I know you specified that you're a US citizen and would like to stay in the US for now - but here's an outline of how things are developing in the UK within the NHS.
In the UK there is a new Scientist Training Programme (STP) in Clinical Bioinformatics with a sub-speciality in Genomics (http://www.nhscareers.nhs.uk/explore-by-career/healthcare-science/careers-in-healthcare-science/careers-in-bioinformatics/bioinformatics-%28genomics%29/), which is 3 years in length and incorporates an MSc. At the end of which the trainees currently have to submit their training portfoilo for accreditation as a Clinical Scientist. You can find last years curriculum here (http://www.networks.nhs.uk/nhs-networks/msc-framework-curricula/documents/STP%20MSc%20Clinical%20Bioinformatics%20-Genomics-%20Final%20Version%201%200%20for%202013%2014.pdf/view?searchterm=clinical%20bioinformatics)
There isn't currently an equivalence process for already qualified applicants to go straight to Clinical Scientist level although the relevant bodies have said that they will put this in place. Most of the current bioinformaticians already in place while the new specialists are trained up have PhDs, although there are exceptions :)
As a registered Clinical Scientist (Bioinformatics) in the UK working in a molecular genetics lab you would probably be involved in various sequencing projects ranging from targeted NGS panels to Whole Exome and Whole Genome studies. I gather that one of the drivers behind the training scheme is the Genomics England 100,000 genomes project and so there should be further investment in the speciality.
The NHS labs work closely with their local universities and generally have the possibility of research projects at the Clinical Scientist level usually based on the speciality of the lab (monogenic diseases, cancer etc.).
Your experience and qualifications sound similar to my own when I was first employed although as time goes on I can see most of these posts going the same way as the Clinical Scientist posts in Genetics - where you either have to go through the training scheme (now 3 years instead of 6) or try for equivalence (the only people I know who did this all had PhDs and postdoctoral experience in human genetics).
I'd be very interested to hear how things are developing in the US especially as there seems to be alot of opportunities. Sorry this is all UK specific but I hope it gives you some ideas.
Edit:: Did some reading around on your Biostars comments and you certainly have enough experience in the right areas to go straight for an existing Band 7 Bioinformatician post in the NHS labs, however the 8a posts I've seen advertised keep asking for a PhD (generally managing a service) - although this is my observations as an applicant not as an employer.
Thanks for the input so far, Garan and Dan. It's been very helpful.