I've heard the Rainmakers with a few different integrateds that a dealer carried. One was from Simaudio (but I think it was the i5 or something like that, probably above your price range). Others were a DK integrated, Music Hall Mambo, and a Jolida 302b. He also had it with Marsh separates (probably available used for under $1K for BOTH amp and preamp).
My favorite combination was the Jolida 302b with the Rainmakers, with the Simaudio in 2nd place, and the rest a close 3rd. The Jolida is exciting and musical, the Mambo a little warm and subdued, the Sim articulate. As I recall, the Marsh and DK sounded very good, but just a half a notch below the rest in terms of the "intriguing factor".
Ultimately, though, as good as the Rainmakers sound for their price and sound, they are limited by their exaggerated mid-bass and lack of full bass extension. Ultimately to get to the next level you'll have to upgrade your speakers.