You can use Hornady .416 or 41 caliber gas checks just fine, but I believe Bullet Swaging Supply has their Gator brand in a 40 caliber diameter also. At any rate, I recommend use of Gator checks in all calibers which they have as they are of top quality, at least equal to Hornady, who makes RCBS and Lyman checks, to Hornacy specs. Perhaps the brightest aspect of Gator checks is the very attractive price without sacrificing quality.
I recommend Wheel Weight alloy for most shooters as they are the cheapest source of suitable lead. But you can use richer alloys if available at a reasonable price.
You'll get more speed from an LBT bullet, and especially gas checked, than with jacketed. Using the slowest powder listed in your manuals for a similar weight jacketed bullet, and increasing the charge till slide recoil is similar, speed will be probably in the area of 150 to 200 fps higher, which make the 10 MM a super hunting defense gun. I suggest a 180 gr weight as it will give adaquate penetration for anything one would probably expect to shoot at, with closest to optimum displacement velocity, or wound diameter, or kill speed, which are all three the same.