Turtle,
You're not using the wrong ball cleaner, simply not following instructions. Wipe the residue clean off each ball, before you play.
ctyhntr might have it right. The Aramith Ball Cleaner has a mild abrasive material in it - you can feel the grit with your fingers - and if you don't polish the balls properly afterwards, it will stay on them and increase the friction instead of decrease it! Of course, higher friction means more throw in pool, but it's especially noticable in games like 3-cushion where it really changes things like the angles off the cushions, how long spin stays on the ball, etc.
However, it could also be a matter of how you're perceiving the speed difference. I doubt ball cleaning has much difference
for a given cloth once rolling has been achieved, since the rolling-without-slipping state is such a low friction state anyways. The sliding state is where friction really matters, and ball-table friction mostly affects how quickly follow and draw take effect. Interestingly, curving is
slower - not faster - with lower friction, since the ball has to spend more time converting the spin into a new direction. It might be that you perceive more exaggerated curves or more momentary follow/draw hesitation as really clean balls being slower, even though the rolling distances will ultimately be farther for a given stroke.
Higher friction also means more spin is worn off with each cushion contact. If you shoot straight into a rail with follow, more follow will remain in the initial direction when there is less friction. That remaining follow slows the ball down until it converts into follow in the new direction, so lower friction means more residual spin and a longer conversion time.
Bob Jewett has a measure of table "speed" where you time a lag shot from the foot rail until it just stops back at the head rail. I can't remember it exactly, but it's something like square the time in seconds and multiply by 2. A higher number means a "faster" table, even though it's slower when looked at in terms of time because the "faster" table lag takes longer! Isn't physics and language fun
Robert