Naproxen is a relative of Ibuprofen - both r primarily anti-inflammatories, they r related so u could try naproxen.
Aspirin is also somewhat similar in action to Naproxen & Ibuprofen, & it has some good analgesic effect as well, so it is a good bet.
Tylenol is not an anti-inflammatory so it will be less effective for ur neck. I would not use it for this.
If u go to things like codiene (available in Canada OTC), u may get pain relief, but poor anti-inflammation so the pain returns as soon as it wears off.
Motrin & Advil r just Ibuprofen under another name, so u r already using those.
Excedrin back & body is aspirin mixed with tylenol. Try the aspirin first, as I said, because tylenol is not going to buy u much.
I think u best bet is taking 2 aspirin with a lot of water next time u have neck pain & see how it responds. You can take more, & aspirin is also a blood thinner so it is decent for preventing strokes & heart attacks. Aspirin is very potent at these kinds of injuries, & was originally ''natural'' (comes from a tree).
In terms of alternative therapies, nothing is going to work like the anti-inflammatories, opiates & then narcotics for neck pain, but ideally u want to stick with the first group.