1. rotate the entire box 90 deg. at a time to see if it helps or changes the distortion. If one position improves it or makes it even worse, then you may have a sagging surround or spider which allows the voice coil to move to one side in the gap. There are ways to re-center the spider but its involved.
2. double check the condition of the surround, either pinch it slightly or push gently on the roll to about 1/4 inch - it should spring back nicely. If it at all dents, crumbles, or doesn't spring back, it and the other driver should have their surrounds replaced with purpose fit new ones. When you bought them, had they been newly refoamed or refoamed a while back? Where do you live and what environmental conditions do these speakers sit in?
3. Order / get from Amazon, Parts Express, or a local Guitar center some DeOxit D5 and use on the L-pad control on the speaker to clean the control, also useful for your controls on receivers and amps. This will ensure the pots are not a source of corrosion induced distortion.
4. If you did move the woofer and the problem follows the woofer only, not the cabinet, I'd not think the crossover is the issue. OTOH, being OCD, I'd look carefully at all the solder joints and wiring connection points and clean them up, resolder them, and make sure the wiring is in good condition.
If after all of the above, the woofer still is having problems, then I would consider the voice coil or spider to be a problem and it would normally need a recone - but hard to find NOS OEM JBL recone kits for this driver, and not inexpensive. Then I would consider buying a used and working 116A or 116H woofer from ebay that hasn't been messed with, and needs a surround replacement, or you could buy one already redone (makes it off time line from your current one though). That's why I suggest replacing the surrounds together. 116A/H drivers on Ebay or even here at AK (become a subscriber, put a WTB in Barter Town Parts and they may come out to play!) are not expensive.
Good luck!