I can't think of any Unique loads that have maxed out accuracy for me in either .44's (Mag or Special). I have had some very excellent light loads of Bullseye, though. I'm guessing the ignition issue mentioned earlier is the fly in the ointment. Bullseye lights up earlier and faster. A magnum primer might complicate the issue by making enough gas to unseat the lightly crimped bullet before the Unique is really burning well. I would try a mild primer like a Federal 150 or a Wolf or Tula LP standard primer.
Find a way to identify each chamber in your cylinder. There may be a zero mark stamped into the ejector, or some other indicator your can find. If not, take a Magic Marker and put a temporary registration mark somewhere. Next, from your 20 remaining rounds, fire a cylinder full for fouling shots, and then fire a cylinder full as you did previously. Use a spotting scope or some binoculars and a piece of paper so you can record which chamber made which hole. Identify the chamber that threw the round closest to the center of the group.
Next, fire a separate group of six onto a separate target with each round loaded only into the chamber that produced the middle hole in the first group. That means loading one in the chamber, shooting it, then opening the cylinder to eject the round and place the next one in the same chamber. If the group you get is tighter than the previous group that used all six chambers, you can see about how much improvement having your chambers reamed will produce. That's always the first step in accurizing a revolver anyway. But if the single-chamber group is no better than the first group, then you probably have the bore constriction issue. If the single-chamber group is somewhat better, but not great, you probably have some of both going on.
This review of cleaners
from a 2006 issue of Precision Shooting concludes that petroleum-based bore cleaning products like Break-Free don't clean carbon well. To get that done, they recommended Slip 2000's product that is currently called Carbon Killer
(it used to have several names they've consolidated). When I got some they sold it as a gas cylinder and piston cleaner. It smells a bit like citrus based paint stripper, and the chemistry seems pretty harsh. I found it slightly etched Parkerizing when an extra long soak (several hours) was required on ancient and heavy carbon cake at the end of a Garand op-rod.
I can also recommend you try Boretech C4 Carbon Remover
. It works very well and is virtually odorless and not harsh on a finish. It came out after that article was written, so they never tried it. The Boretech stuff has good corrosion inhibitors and you can leave it in a bore indefinitely.
If you want a CLP, try Gunzilla
. It also attacks carbon well, but is just slower working than the other two products. I've had good luck leaving it sitting overnight or longer on old carbon. If you buy their little pump spray bottle and get it on the gun and in the bore at the range, while the carbon is still soft (it hardens over time), you'll be amazed how much more easily it comes off by the time you get it home. It leaves a lubricating film behind that doesn't attract dust.
If you want a general purpose cleaning product that gets copper and lead as well as carbon, Boretech Eliminator
, mentioned in the article, is the one I use for general purpose cleaning. It's carbon removal isn't as good as the separate Boretech Carbon Remover product, and its attack on copper isn't as rabid as, say, KG-12, but for a jack of all trades (except lubrication) cleaning product it is hard to beat. It's another I keep in a pump sprayer and apply to rifle bores at the range. By the time I get home, they're pretty much cleaned with a couple of fresh patches.
Anyway, there are new and much faster cleaners now available. One thing you can do with BF CLP is shake the bottle well to suspend the Teflon, then mix a slurry of it with JB Bore Compound and put it on all the moving parts of your model 29 action like it were a grease, then close the gun back up and dryfire it double-action like this until you feel the JB wear out. This is a S&W armorer's school trick for smoothing up double-actions, in particular. The JB breaks down and polishes while the Teflon gets worked into the surface of the metal as a permanent lubrication. It does make the actions feel very smooth.