Sway is caused by a variety of factors. Sway is the ability of the trailer to move the rear of the tow vehicle over the axle of the tow vehicle. It can be caused by improper loading of the trailer (not enough weight on the tongue), but it can also be caused by low or unequal tire pressures on either or both the tow vehicle and the trailer.
So, presuming that your tire pressures are at or near max (especially on the tow vehicle), and since you didn't experience sway without the suspension mod and have it now, and since you mentioned the "tongue height" issue, my guess is that you probably are now towing in a "tongue high" attitude. New, your tongue height was probably 19". As a result of the start of axle rubber failure, your actual tongue height may now be as low as 17", but if you have it set at 19" you could be as much as 2" out of balance tongue high. The shift in weight being as much as 2" tongue high might very well be enough to cause sway issues.
Measure your frame at the tongue and bumper while the trailer is on level ground to make sure it's level. The distance from the ground to the top of the hitch connector will be your actual tongue height now.
If, in fact, the new measurement is around 17" when the spec sheet says it ought to be 19", you're probably getting due for an axle replacement, and that wouldn't be unusual for a trailer that's over 20 years old.
The answer to your last question about the dual cam setup... I'd certainly recommend it AFTER you figure out why the trailer is swaying. Sway controls mask the bad stuff that happens until it can't mask it any more. Then you're REALLY in trouble. If you sort out your issues BEFORE you use sway control, then the sway control merely gives you an added measure of safety.
Good luck and keep us posted!
AIR 2053 Current: 2004 Airstream Interstate "B-Van" T1N Sprinter & 2006 Born Free 32 RQ Kodiak Chassis
Former Airstreams: 1953 Flying Cloud, 1957 Overlander, 1961 Bambi, 1970 Safari Special, 1978 Argosy Minuet, 1985 325 Moho, 1994 Limited 34' Two-door, 1994 B190 "B-Van"