The easiest fix is to put a tiny smear of lube on the base of the bullet before seating the gc. They will stay on until you get them seated in the case if you don't bang them around. When checks are hanging on loosly like this, do not seat them below the neck on bottle neck cartridges if the powder charge isn't compressed to hold the checks in place.
Understand that loose gas checks get tight real quick when the powder blast hits them and cannot come off inside the gun while traversing the bore. Average rifling depth is around .008, and will crimp them to the bullet tightly enough in most cases to get good accuracy and help impart rotational force to the bullet, which is one of the major functions of a gas check. I cut all check shanks straight for maximum grip on the check, to allow maximum possible velocity potential. Most mold makers taper the check shank to keep customers happy, because checks will almost always hang on , but they don't get a good enough grip to impart rotational force if the shank is a bit smallish. Because of tapered check shanks, many people don't get the performance potential of gas checks, so prefer to use plain base and live with the lower velocity potential.
Old Lyman checks were thinner metal than Hornady checks, but all currently made checks from both Lyman and RCBS are made by Hornady and to Hornady specs. I therefore cut all my molds to take Hornady checks, and for the 41 pistol or 10MM, 416 checks are the ones to buy. Gator 41 checks are high quality and close to the same specs as Hornady. You might check on their cost.
Your game performance is typical for my bullet designs. Am assuming you weren't loaded to max, which is fine if you get a 3/4 inch wound channel or have the LFN in 41. A one inch wound in normal for full loads with the LFN and a bit larger with the WFN. Of coarse 44 and 45 wounds with the same profile bullets are larger. With one inch to 1 1/4 inch wounds, animals rarely move out of sight after taking a hit anywhere in the vitals.