All of our kits will come with the modern accl pump assembly with the latest design Viton seal, and new springs/retainer. Change all the parts, and gently form a new seat in the casting with the old check-ball.
I would NOT use the check valve, they are very restrictive. Fuel draining out of the bowl is most likely a leaking bottom plug. It can only drain back a small amount anyhow, as the fuel inlet seat sits pretty high in the carburetor. It can't drain back at all if you leave the clip off the needle during assembly.
If it runs fine in all areas I would not change the jets and metering rods. If it seems lacking anyplace, or exhibits any lean conditions, they tune it accordingly. The carburetor number that you provided is a "Service Replacement", so I'm not exactly sure how it is set up from the factory, the liturature that I have doesn't include those part numbers. If I were building it here, it would get new jets and metering rods, based on the size of the main airbleeds, and the engine specs. If you can provide the MAB sizes when ordering, we can supply the correct jets and metering rods for what you are doing.......Cliff