You could be correct. A rear end will howl when there's too little backlash between the ring and pinion. It has to be a little bit loose or you'll get that nice howl once you start moving. For some, it's worse when accelerating, for some it's worse when decelerating / coasting. If it's worse when the rear end is hot (after you've been driving for a while), it might point to the backlash setting (gears tighten as they get warmer).
Backlash problems can be cause by shimming the carrier poorly left-to-right, and also if the pinion depth hasn't been shimmed properly front to back. Or a combination of the two.
It's pretty easy to check backlash with a proper (magnetic mount) dial indicator. This can be done by just removing the differential cover, draining the grease, and measuring the motion.
You can also check the contact pattern of the gears with some marking compound (in a pinch anti-seize or zinc oxide creme (like diaper rash creme)) will also work. But you have to know what to look for. It's also important to see if you have some bad wear, incorrectly set backlash can chew up the gears pretty quickly.
There are other things that can cause a rear to howl - bearings (pinion, carrier, or wheel), road noise from aggressive tires, even exhaust drone.
If I had to guess, since the gears are aftermarket, they were probably installed poorly. It's generally a job for the pros, though if you're mechanically inclined it's not all that hard to do. If you're not experienced, it may be better to have a good, trusted shop take a look for you. I definitely wouldn't throw money at it because the noise could be from a lot of causes.
Generally (very generally) rear end noises don't much respond to a lubrication change. Unless it's very contaminated, the wrong viscosity, or wrong type (no friction modifier in a limited slip for example). But long story short, the fluid has to come out if the noise is coming from the diff, and you (or a skilled mechanic) can determine whether it needs more work before filling it back up again.