If I don't want to change the original set up, what would the best strings for playing jazz be on a USA ASAT Bluesboy Classic semi hollow?

The setup will drift eventually, its unavoidable. If you want to keep it as long as possible then stick to 10-46s. Changing the string gauge will throw the original setup quicker but luckily there are easy ways to get it back.

As for jazz, you can use any strings you want. Some jazz guys use thick, flatwound strings, others don't. They might play a hollow archtop too, and the Bluesboy will never sound like one of them.

some halfwound strings might get you a little mellower tone as will pure nickels. the halfwound is kind of ground down string that feels similar to flatwounds.

It's interesting you mention pure nickles. I was going to ask about them. Someone recommended them to me, and I have been tempted to try them. I play mostly blues oriented styles and use D'Addario XL Nickle wound. What difference would I likely notice on an ASAT Classic with pure nickle? D'Addario makes a pure nickle set. The guages are slightly different I notice .... 10-46/10-45....and the tension looks to be slightly less with the pure nickle.

Try GHS Electric Guitar Nickel Rockers Rollerwound Light, .010 - .046, R Plus RL

http://www.juststrings.com/ghs-r-plus-rl.html

I use them on one of my guitars, I like them.

How would you describe the difference between the pure nickle and the nickle-plated? I read descriptions like "more mellow", "more sustain", "less distortion".

I'll probably just buy a set and give 'em a try.