If that liner is the one made by Jim Chambers, with the parabolic cone on the inside, it will definitely help.
As to the delay in ignition, delays come at different times, depending on lock geometry, vent hold placement, and where powder is put in the pan.
With an empty gun, in a dark room, hold the gun out at arm's length, so you are looking at the lock from the side. Use your Left thumb to trip the cock, and throw sparks. Do the sparks get thrown into the pan directly, or do they roll down the face of the frizzen, and eventually fall into the pan? If the later, the problem is lock geometry, and the angle of the flint to the face of the frizzen is to " square ". If you don't already have them, you will begin to see gouges in the frizzen face at right angles to the length of the frizzen, where the edge of the flint is striking the face. Get a protractor at the grocery store for under $1.00. Lay the gun on its side, and place the protrator so that the center of the bottom line( where the hole is) is at the point where the flint touches the face when lowered. You want to grasp the gun and lock so your hand helps to hold the frizzen closed under the spring tension against the cock, so that your other hand can postion the protrator, and then use a straight edge to run from that center point up to the top of the face of the frizzen. The straight line should cross the outer ring of the protractor, and tell what that angle is. If its not 55-60 degrees, the flint is striking too square.
To fix; make a template on cardboard, using a heavy wide magic marker pen to give you the 60 degree angle you want the cock to strike the frizzen. My template shows the shape of the cock, and more importantly the angles of the cock screw as it goes through the lower jaw, with a line drawn on that axis down through the lower part of the cock. I show on the template the current angle of the lower jaw to this axis, and then draw in my heavy line to represent the new angle I want to achieve. When working on the cock, I can remove it from my vise, place it on the template, and check to see that I have achieved the angles I want.
Remove the cock from the lock, and remove the top jaw, cock screw, flint and flint wrap. Then using a propane torch on the narrow part of the goose neck of the cock, heat it to cherry red/orange, and use plyers to bend it forward to meet that template. With the thinnest point of the gooseneck heated this way, you should be able to bend the cock forward by putting pressure on the lower jaw of the cock, without resorting to using a hammer. If it won't bend, keep heating the gooseneck. You may want to enlist the aid of a helper to hold the torch on the gooseneck, while you are doing the bending.
The amount of bending required is very little, so don't use a lot of force at first. See just how much force is needed to move the metal before putting your weight on it.
When the bend is made, just let the cock cool in the air. It will take about 20 minutes for it to be cool enough to touch. If you leave it on a vise, or other heavy metal surface, it will cool much faster, as the metal will act as a heat " sink ". Clean off any scale that forms where you heated the cock, and touch up your browning, if that is how the cock is finished. Then replace the cock on the tumler, and put the top jaw, flint and wrap, and cock screw back in the cock. You should be ready to go.
We have previously talked about positioning the touch hole above your pan, so that the hot part of the flame from the burning powder is next to the hole, and about using a vent pick to open a hole in the powder. You may be allowing crud to build up in that gun by cleaning it only after 15 rounds or so, and that can cause hangfires, too. It all depends on how close the face of the breechplug is to that vent hole. If its really close, any buildup will block a portion of the hole, and inhibit ignition. Ideally, the face of the breechplug should be about 1/16 inch to the rear of the rear edge of the vent hole, so that crud build up does not cause hangfires. Since you did not make the gun, this is a hard thing to correct. However, you can clean between shots, and that should help eliminate those kind of hangfires. You just have to use the right jags, the right size patches, and learn how to adjust your stroke so that you are pulling the crud out, and not pushing it in.
If I waited 15 shots before cleaning, It would take me 5 or more patches to clean the entire length of the barrel, as I would want a very clean patch to get down to that last 2 inches of barrel to clean the face of the breechplug, and the chamber( which should have burned most of the crud out!) I do short strokes when I am cleaning a dirty gun barrel, never going more than 6 inches down before pulling the patch out and the crud in that section of the barrel with the patch. Then I change to a new patch for the next section. When I finally am down to that last section of the chamber, and the face of the breechplug, I slowly push the rod down, and then turn the jag clockwise, to clean off the face of the breechplug. Because the patch is not already full of crud, the cloth soaks up any crud on the face of the breechplug, and I can pull it out. If its particularly messy, as on high humidity days, I will then use a clean patch with moose milk on it, to dissolve the remaining crud down there. Then I use a couple of clean patches to pull out the solvent, and any crud, and dry the chamber, so I can load the next powder charge into a dry barrel.
When cleaing between shots, there is much less crud in the barrel to clean out, so I can get by with using only one or two patches, again using short strokes to clean the first 6 inches or so, then the next section, If I see a lot of crud building, I will either turn the patch over, or get a new patch. It all depends on the condition of the patch at that point. Being a cheap fellow, I tend to flip my patches over.
I found that if I did less, the gun would occasionally hangfire on me. I also found that cleaning the barrel between shots involved a lot less work, and a lot less problems to solve. But, I do go through cleaning patches, and that seems to be a problem for some shooters.
YOu can throw flannel cotton patches into a clothes net bag, and wash them in your washing machine( be sure to wipe up the grime and soot that will be in the tub when it finishes, if you want to be able to continue to live with your domestic supervisor!) and they can be dried and used again. I haven't done that, but I have known shooters who do. After a second or third use, they finally throw them away.
I hope this helps.