First off your Snell K2's are awesome sounding 2 ways. Detailed, wide soundstage, speedy, dynamic and well controlled tight bass. Back in the mid 90's I sooo wanted to purchse them, but was putting the ex through college and....
So onto the amp. You have a few options to play with and everything being system dependent I would try them all and find which way you like. You can run a second set of speaker wire from the Main Speaker Out to the Speaker Level In on the sub, and then try from the remote speaker outs. Using the Main Speaker Out will give you the same signal the K2's see. You can also use a speaker to line level RCA converter (not expensive and can be found from car audio dealers)and try the line level input on the sub. Or just try the Pre Out and judge for yourself. If you decide to go with a line level input I would seriously recommend a Dspeaker Antimode 8033c. I use the "s" version with my two subs and have the best bass I've ever had. Dspeaker also makes a summing cable that you can run from your main speaker outs and converts to and RCA end to fit the Antimode.
As for carpet vs solid floor that all depends on the sub and the kind of bass you like. I've had a number of subs over the last 25yrs and some were better forward facing some better down facing on hardwood and some better facing carpet. As noted it is all system and listener dependent.
Hope this helps and Good luck