You said the drill wandered a bit and ended up lower than you wanted it. You didn't say how much lower and that does have some bearing on the answer.
You also said the hole ended up at an angle that was slightly downward. Again, this will have something to do with a good answer.
If the mouth of the hole is a little low but it is above the bottom of the pan it should not cause a significant problem with ignition.
What might be causing the slow/hang fires is the size of the hole.
As you may have noticed, most of the vent liners used work so well because they are relieved or hollowed out on the inside. This places the powder charge within 1/16" of the outside of the barrel and a 1/16" diameter touch hole presents a goodly amount of powder directly to the blast from the pans flash.
With your non-liner hole the barrel wall is at least .200 thick and because the inside of the hole is not relieved the powder from the main charge is also at least .200 from the pans flash.
Add to this the fact that as the pans flash travels thru that 1/16" diameter X .200+" long hole it is rapidly loosing heat to the walls of the hole.
Combining these two things it is little wonder that the ignition is erratic.
To fix this condition my first recommendation would be to enlarge the holes size to 5/64" and try the gun. It should show significant improvement.
If it still isn't living up to your expectations the only easy fix is to replace the hole with a vent.
Here is where things can get sticky because the liners tap drill will want to follow the existing touch hole.
If the height of the hole isn't more than 1/32 below the upper surface of the pan then it would still be OK for a liner. If it is 1/16 below the top of the pan you will have to use your own judgment.
Before thinking of a liner you will also have to measure the center of the touch hole to the face of the breech plug. Do this by running a rod down the bore and by making a mark that is flush with the muzzle on the rod. Then, hold the rod along side the barrel aligning the muzzle mark and notice where the touch hole is relative to the end of the barrel. If the distance is more than 3/16" your good to go with a 5/16" or 3/8" liner.
If the distance is greater than 1/8" you can use a 1/4-28 liner which some folks think looks better.
Now you will have to decide if the angle of the existing hole will cause a problem with the threads for the liner.
If the angle will not cause the tap to run into the bottom of the barrel you should not have a problem.
If no potential problem exists then use the correct tap drill and tap to create the new threads for your liner.
After it is installed you will need to file the outer face of the liner flush with the flat on your barrel but that shouldn't be a big deal provided you protect the adjacent areas with masking tape or something similar to protect the browning from the file.
If the fore/aft, up/down or angle is going to cause a problem with a threaded liner you will have to have the new liners threads drilled in the "correct place" and at the correct angle.
This is why the other folks are talking about using a milling machine to redrill the hole for the threaded liner.
Only a milling machine has the rigid strength needed to keep the new hole where it is supposed to be because, as I mentioned, the tap drill will try to follow the existing hole.
Let us know what you decide and how things work out.