Help this Noob assemble a 7.1 system. Will this work?

Welcom to the club Hiccups. Sorry I am not very qualified to give much advice, but I'll do my best. I'm surprised no one else has reponded to this. Most times everyone in here are very helpfull with these questions. First the impedance question. My non expert guess would be yes with a little care. This is all from memory from research I did some time ago so...Speaker impedance will vary depending on the signal feeding it. So a 4 ohm rated speaker is not always going to be at a true 4 ohm load. Cheap speakers could drop to 2 ohms or less. The lower the impedance the higher the output from the amp. Do you see how this could lead to a problem? With speakers such as the LSi and quality amplification, as long as you do not get crazy with the volume you would probably be ok. But you might want to try the "Basic Hookup/Wiring Questions" and/or "Troubleshooting" forums on this board, or email Polk and ask them. I used a Denon AVR 2000 rated @80W into 8 ohms to drive a pair of Genesis Physics 320, (very similar specs to the LSi15s) 4 ohm speakers recomended power 20 - 250 W for about 20 years before the foam surrounds gave out. As soon as I get time I will be replacing them and put them back in use. For now I have replaced them with a pair of Polk Monitor 50s. Then I'll probably upgrade from plain and simple Dolby Pro-Logic to a new 6.1 or 7.1 receiver.
But back to you, I looked at the list price of items on your list (I hope you don't have to pay list for everything in Alaska) but it's obvious you're ready to drop some serious $$. I would say you should be able to have a great sounding sys. in that price range. As far as power I don't think you have any problem there. You are off to a good start by doing some research. You might also want to try http://www.avsforum.com or any/all of the numerous forums on line. Most are full of people willing to help especially when it comes to spending other peoples money on equipment. Always someone there to tell you that will be good but for $100 or $300 more you could get a ...... Also search for user reviews on any thing you might be interested in. Just don't base any decisions on one or two comments. Try to find as many as poss. and look for trends or comments good and bad that keep repeating over and over. I have heard many times, "Buy as much power as you can afford" which is probably true. But keep in mind that good CLEAN power cabable of quickly and cleanly hitting short peek requirements is as much if not more important than total raw power. A quality 40W amp can outperform a cheap 1000W amp outputting crap. I just suggest here don't get caught up in the $$ = braggin' rights trap. Also keep in mind that your room size, shape, building materials, furnishing and speaker placement are going to play a part in the end product reaching your ears. IMHO once you hit a certain price range you should look more for reliability, the SQ will be there. I can't hear the difference between a $2,000 system and a $10,000 system, at least not a $8,000 difference. Maybe I spent too much time working under jet aircraft and listening to live rock&roll, but I don't think I ever could. There are some that will tell you they can hear the difference "breaking in" cables will make. They are lucky to have such keen hearing. I'm lucky because I get good sound (to me) at 1/3 of the price and only feel the need to upgrade something every 10 or so years.
I am confused on why you feel you need the Rotel RMB-1075 amp. I think the Onkyo could do a fine job on it's own. Are you planning on using the Onkyo as a pre-amp, and to drive your rear surrounds? I think the Rotel is a only a 5 channel amp. How big of a room are you looking at? Good luck with your search, and hope you enjoy the new home and what ever you decide on.

Yes!Definitely get an amp. That's too much LSI goodness for a receiver.... And welcome.

Welcome Hiccups!

You will have one slamming system. But as others have suggested you should up the amp to a Rotel 1095. Other good amp choices are Outlaw Audio 7700, Any 7 channel amp from Sunfire, or Parasound.

Once again welcome to club Polk. And when you put it all together...PICS!!!!!