Ramjets, Kodiaks, Crow Mags, Daisy pointed, Benjamin, Crosman tried....
Barrel is recrowned.
I've tried all of the above also and then some,
and seem to have the same problems that you have.
I have LE # 359 , it was modified by Skyler to
get more power with fewer pumps and 3 pumps
is plenty for backyard plinking and targets.
I bought a variety pellet pack from Straight Shooters
and found that the JSB exact Jumbo Express Pellets
give me the Best groupings with this gun.
I am also shooting at about 17 yards,
this gun goes about 490 fps at 3 pumps.
Beeman H&N Match pellets group well,
and the Plastic Nose Predators are about as
good as the Express pellets.
The problem is.... the Predators are a Bullseye
the Express is High and to the right.....
and the Match pellets are low of point of aim,
with a flyaway now and then.
4 or 5 pumps changes everything, and
I'm about Scared to pump this thing past 6 pumps.
At 6 pumps I have had the Bolt to Blow back
on me a couple of times.
Guess I'll just spope it in on BullsEye with the Express
pellets , and use the Mil Dots to adjust for the others.
Crossman, ( any kind ) Daisy Match, and Ram Jet
pellets gave the worst results in this gun.
One other Notable Good Mention, is the Stratton by JSB.
Keep Shootin' and let us know how it goes.