Since everyone is tossing in $.02, here's mine.
I've heard this setup with my Polk speakers, although they are '88 model RTA 11tl's (heavily tweaked) not the more current LSi series. To me, it sounded excellent and the only reason I didn't keep the amps is because I really like the Odyssey Stratos Stereo Extreme much more.
You may be able to get this preamp for the price it was going for about 6 months ago or there is a used one on Agon -
http://cgi.audiogon.com/cgi-bin/cl.pl?preatube&1069906453 , more info at
http://www.phillyaudio.com . Typically $350, I'd spend another $50 on a quad of 4 Tung Sol 2C51/396a NOS tubes, for a total of $400. If you go with this preamp I can let you know where to grab those tubes from.
Then you could go with Scott Nixon Monoblock amps. VERY musical, great sound, the Polks are pretty efficient so you should be fine SPL wise. They are clean, quiet and great little amps.
That combination should put you right at $1000 or so. Another combo I would HIGHLY recommend which is almost what I've got is the Philly preamp with Klaus' new Khartago amp. That'd probably set you back a bit more, around $1100 - $1150 or so, however, you'd have that Odyssey "non" sound and extreme quality and some extra watts.
If you want something to front the Polks that will do them service you won't go wrong with either of these combos.