re:
"Little to no barrel hood movement."
Meaning...Is there any movement or not? If there is...even the tiniest bit...you're at the limit on vertical adjustment, and even if it's right on the edge of downward movement, your aggregate vertical dimensions are giving you all the lockup you'll get with that barrel in that gun...at least without some pretty extensive work. Welding the lower lug to get the barrel to sit higher in the slide. Swaging the frame rails down to get the slide to sit lower on the frame in order to take up the slack, and then maybe filing the slots between lugs a little deeper in order to adjust the barrel's final height...or all of the above.
Off-center firing pin hits generally aren't too much of a concern as long as it's not TOO far off. Since the gun is shooting 4 inches higher, it indicates that the barrel isn't tilting upward into lockup quite as much as the other one was.
A .200 inch diameter slidestop pin will raise it by half the amount of the difference between the original and the new one...probably not more than .002 inch. Not enough to make a practical difference.
Sounds like you need a hard-fit barrel to bring everything into line. Sometimes that's the way it goes though...Tolerance stacking can work for you or against you. Luck of the draw.
More of a concern is how much vertical lug engagement is there...and how many lugs are taking the shock of recoil in the horizontal lockup. You'll need to gauge the slide and barrel to find out how they're doin' in the horizontal...but the vertical is a little easier.
Draw the slide to the rear far enough to slip in a piece of wood or flat metal stock that's about 1/8th inch thick and let the slide rest against it. Measure from the top of the slide to the top of the barrel hood. Remove the shim and let the slide go to battery, and measure again. The difference is the depth of lug engagement. .045 to .050 is good. That's pretty close to 100%. If you've got at least two lugs bearing equally in the horizontal plane, you're good to go with a little less...about .042 inch. With all three...which isn't likely with a drop-in barrel...you can go down to .040 and still be okay for standard-pressure ammo. With only one lug bearing the brunt...AND less than .045 vertical engagement, you can expect shortened barrel life due to increasing headspace as the gun is fired. Ask the smith what the headspace was in the new barrel. If he didn't gauge it exactly, have him do it, and have him check the horizontal engagement too, if he has the gauges.