I don't have sleep apnea, am not overweight, sleep on side, don't drink, but still snore when breathing through my mouth. What aids should I try? Mouthpiece keeping jaw forward? Strap to close mouth?

Sleep study? Did you officially have a sleep study? Seems you have tried a lot of remedies to try and help, but need to know for sure. CPAP is the "gold standard" of care, but dental mouthpieces for snoring and mild sleep apnea are very effective.
Can try mouthpiece. how do you know you don't have sleep apnea, have you been tested? if it is primary snoring you could try Theravent, or you could try an oral appliance. There are many options out there.
Snoring. Reduce alcohol intake to reduce snoring. Alcohol relaxes the muscles in the back of the throat which leads to snoring. Sleep deprived people sleep harder and snore more. Upper airway narrowing from congestion, deviated septum, and tonsils can lead to snoring too. See an ENT physician who specializes in sleep disorders.
Snoring . If you snore at night and it is effecting your spouses sleep, you can try a fan or some white noise with a radio of sound machine from the sharper image. Are you well rested when you wake up. Do you have long pauses when you sleep? What is you epworth sleep scale number? You can get the questionnaire on line. If you are over10 you should get a sleep study. Dental appliances can help, expensive.