I can't say that I have respect for every pulmonary specialist I've worked with (as a respiratory therapist), so I hope (maybe word of mouth?) will get you a better one. Regardless of who you get, why in the world would you need another sleep study? That tells me that they didn't get enough information (couldn't get you to sleep 4 hours or more) or couldn't apply positive pressure to the inside of your airway through the mask such that it resulted in showing what final pressure you needed to get quality sleep.
Oxygen saturation read through the fingernail should be higher than 88%. You may have needed oxygen titrated, which means that in addition to the pressure from the machine, you needed to have some flow of supplemental oxygen mixed into the CPAP or BiPAP pressures (BiPAP refers to a higher pressure during the "inhaling" phase.) The newer CPAP or BiPAPs also can self adjust (some nights you may need to have a little extra pressure and believe it or not, little tests during the operations will result in the adjustments you need for that particular night when maybe you're super somnolent.
Regarding dental appliances for sleep apnea, some devices are good, depending what kind of distance there is between the chin and the jaw (which is roughly the center of your airway). Some mandible advancer mouth pieces can achieve a more open airway, but they are NOT as effective as CPAP or BiPAP.
Here's a link worth a look: http://www.sleep-apnea-guide.com/mandibular-advancement-device.html
Just think.. with a good pulmonary doc, you'll have an explanation of this, and real quality sleep will lead to quality wakefulness!