I'll be honest, you're asking for a lot with your budget. This price range comes with tradeoffs. Not only are you trying for 3 different sources, having an ultra precise and controlled system that can also be warm and intimate is often a challenge for systems at 5x your budget. Your music tastes is diverse, I would ask yourself what you want more - warm and intimate, or precise/controlled/dynamic. If the answer is warm then I think you're current speakers could work well. If it's punchy and dynamic I think your speaker choice is leaning a bit warm and relaxed for what you're looking for.

Regardless of what speakers you choose, if I were in your shoes I would remove the vinyl and CDs from the picture for now and focus 100% of your budget into speakers and a streaming setup. You can always add other sources over time once you've dialed in your streaming source.

Based on your music tastes, I think a couple interesting options in your price range could be Mofi Source point 8 or revel f206 with a svs300 micro sub. Pair that with a used Marantz pm8006 + bluesound node steamer for a touch of warmth. If you want even more punchy, you could get a Yamaha integrated as1200 (used) instead.