Since you're asking about an integrated amp as an option, I'll assume 2-channel performance is important to you. I think if you were to spend that kind of money on a stereo preamp it would outclass your amp, which is a good amp for the money but there are limits. So for this reason I'd definitely go the integrated route. Your speakers benefit from a good amount of power, and if you're looking for a more neutral and detailed sound there's a Hegel H360 available here now in your price range. If you'd like a little warmer, richer, or fuller sound there's a Plinius Hautonga also available here now (there are good reviews out there on both if you're interested). I think you'd notice a very big improvement with either of these as they are both fantastic integrateds, but it just depends on what type of sound you prefer. Obviously there are other great choices out there, but these were just two I found with a quick search here. I believe both of these have a HT bypass function, which is obviously nice to have in your situation.
If multichannel is very important to you or you're not happy with your current multichannel performance you could also go for a good prepro, but good ones are pricey and I'd still look to at least add a good stereo amp at some point in the future. Basically, you'd be paying A LOT more to boost your surround performance versus just adding a good integrated as above. Just depends on what you're looking for. Hope this helps somewhat, and best of luck.
If multichannel is very important to you or you're not happy with your current multichannel performance you could also go for a good prepro, but good ones are pricey and I'd still look to at least add a good stereo amp at some point in the future. Basically, you'd be paying A LOT more to boost your surround performance versus just adding a good integrated as above. Just depends on what you're looking for. Hope this helps somewhat, and best of luck.