Hi fishtaco,
Its not really my area as I'm not an orthopaedic surgeon or sports physician but I've heard some good things about PRP. Your right though about the lack of evidence for it at the moment so best thing would be to see does your insurance cover it. Worst thing they can say is no!
However (and this is only my viewpoint) I think that PRP may not be as effective for tendinopathies as it is for treating acute or some other chronic inuries due to the fact that most tendinopathies are actually tendonosis (degeneration of the tendon - replacment of 'good/normal' collagen with 'poor/abnormal' collagen) and you don't need more collagen (tendon tissue) but rather the right type of collagen. Also there is a theory that tendinopathy pain is largely due to ingrowth of blood vessels and nerves into the tendon in responce to prolonged overuse, in this case sclerosing or high volume injections may be more effective.
As is said injections arn't really my area so you'd need to talk to a specialist. Personally I'd give it the 12 weeks and see how it is then.