If you are passing the tests, then it's probably just a matter of keeping at it until a company has a suitable opening at the time you apply.
If you are not passing the tests, then it has nothing to do with the companies not "having the time" to hire you. If your program didn't train you well enough, you will continue to struggle to find employment.
Companies are offshoring, healthcare providers are adopting recordkeeping systems that employ voice recognition and point-and-click template data entry and other technologies. This has left a large number of experienced US MTs scrambling for a shrinking pool of MT jobs. Your competition has years of experience to offer. That's probably the main obstacle for newbies. Companies have their pick of people who can hit the ground running and won't need any remedial training or handholding.