So I am taking this to mean you have no opportunity to do a free trial of the machine? That certainly makes it more difficult.
As for a prescription the way it works in Canada is that your doctor gets the sleep test report. If it indicates apnea and they believe a CPAP is suitable, the doctor just signs it and it becomes a prescription. I would think it is similar in the US, and the doctor involved is obligated to provide you a prescription even if they don't sell you the machine. Kind of like a prescription for a medication.
As for a machine, your issue is essentially hypopnea and not apnea. Not all machines detect and treat hypopnea as well as full obstructive apnea. I think the best auto CPAP on the market is the ResMed AirSense 10 AutoSet. From testing it does treat hypopnea well, and it is good at reporting hypopnea, obstructive apnea, central apnea, snoring, flow limitation, and other variables. It is compatible with SleepyHead so you can take the SD card from the machine and read it with SleepyHead to get your detailed results.
I see that CPAP.com offers a 30 day free return policy. So I guess one could buy the machine, try it, view the results on SleepyHead, and then decide if an APAP is really necessary, and if you can tolerate it.
Here is a link to the machine at CPAP.com. I would suggest the "For Her" version even if you are male. It has an optional extra program that you can try to see if it works better than the standard program. Unlike places in Canada, this outlet does not seem to offer packages. This appears to be just for the machine standard hose, and no mask. Most will want a heated hose for comfort, and that is an extra $40. A basic mask would be the ResMed AirFit P10, and it is $100. It comes with a fit pack which means it includes the small medium and large inserts, and you use the one that fits you the best. But, I would look around. In Canada you can get the machine, heated hose, and mask for about $900 CDN ($660 US). There may be better prices in the US. But perhaps at CPAP.com you are paying extra for the 30 day ability to return and get your money back. In any case here is the link:
ResMed AirSense 10 AutoSet For Her