Looking at cylinder specs, both the Luxfer and Catalina AL19s are neutral when empty and -1.3lbs when full (with the valve included). That means you'll be a little over a pound heavy on the side you sling the bottle. I would try just keeping more air in that side of the wing/bladder. If you are trying to stay still in perfect trim, and pushing the bubble to the side of the wing the pony is on isn't working, you could shift a pound to the opposite side. That will even you out when it's full, but you'll run back into the same problem when it's empty.
Really though, 1lb shouldn't be that significant.
-1.3lbs does not include the reg, which may be an additional 2-3lbs. 3-4 lbs offset; that's a lot of offset in trim. If you're sporting a stock Jacket BC, you're going to have to offset your weight placement.
Keep in mind your SPG or console clipped to the left side also has negative bouyancy, normally it's so minimal that you don't notice, but it does add up into the equation as well.
If you're using a Back-inflate, wing, or drysuit, you can compensate with an offset air bubble so long as you're not in the (-)4-5 lbs offset range. If you're in that range it becomes more of a burden, especially in a drysuit.
We use 13cuft ponys on my work's Jacket BC's and I have to offset 4 lbs to keep from rolling.
We use Sherwood Brut regs with a Button SPG & Second Stage; which doesn't necessarily put it on the heavy spectrum of regs. The 13's are -2.1 full though, unlike the 19.
With a Jacket BC, your pony bottle will also be blocking your weight pockets. This could make ditching or weight recovery complicated. So adding a weight belt may be preferable to split up your weight. But then you also need to learn a weightbelt roll recovery if your belt ever comes undone. Because standing on the bottom to lift a weight belt behind your back doesn't work on the anchor line.
Then there's the issue of handing off your pony when you're terribly offset. Not a huge issue if you're sticking to no-deco diving, but it does mean to be safe, you have to be 3-4lbs overweighted and offset.