I use the Scosche Rythm+ with my Garmin 610 as I find the chest monitors very uncomfortable. If anything, for me it looks like there are less anomalous results (weird jumps etc) than with the garmin chest straps, but I have no way of proving whether it is more or less accurate etc. I do find it extremely comfortable, and would not swap back now. I managed to get a good deal on a new one from ebay after a couple of weeks of looking for one. I too recommend DC Rainmaker for reviews...far more up on the technical nature of these things then I could ever be!!
The frustration is horrible, I completely understand that. I hope you can get a referral quickly. I had the same frustration with waiting (and the fact that my GP wouldn't refer, but that's another story). In the end I hadn't run in so long I worked out I'd have purchased at least two pairs of trainers in that time, and stuck the first two sessions of physio on a credit card (less than one pair of shoes), and in the end I had four sessions totalling £120, and the last one was for my own peace of mind, so could've got away with 3. I know that may not help you, but I do understand where you are coming from. Good luck and take care.
I know you said you don't want a physio referral, but it might be your best option. A decent sports physio will almost certainly be able to help you find a diagnosis. In fact they are likely to have more of a clue than the average GP when it comes to it. Strength training will only help if you are targeting the right bits, and a physio would help you do this. Some strength training could exacerbate your problem if you are tightening up the wrong bits.
I struggled with a bad knee for a good couple of years before finding myself in the office of a decent sports physio. Within a couple of weeks it was starting to feel much better and after a few months everything is good. Ask local runners for recommendations.
It may be worth getting a second opinion on your orthotics. I've just posted on another thread about how I had trouble for ages, but a change of physio and pod has solved the problem completely.
I used to have the most built up orthotics imaginable, which despite lots of adjustments gave me terrible blisters and didn't help solve the problem. A new physio/pod combo changed my style of orthotics completely and they now look very minimal,and work in a different way to my old ones, but videos of me running show an enormous change in how my feet/legs function. I have also been pretty dedicated with pilates and exercises that my physio gives me and both pod and physio say these are really helping too. I believe them because I have no more pain. Initially I was not best pleased that the pod wanted to change my orthotics because I had paid for the other ones in good faith, and had to pay again, but I tell you, it was worth it.