Personally, I think Thiels should be paired with an amp that costs at least as much as the speakers themselves. Some systems work with 50% system budget going to the speakers and 50% at everything else. Some people build very fine sounding systems that way. It just doesn't work with Thiels
I own Thiel 2.4s and my amplification (ARC pre and amp) are 4X the price of the Thiels and the 2.4s keep up very nicely. Tobuns is exactly right. Thiels are very transparent and require high quality amplification. I think the Rotel 1095/Thiel 1.6 combo may sound a bit lean or to some analytical. What i would do is put the Rotel up for sale and add the proceeds to your $2K budget and buy a used Pathos Logos integrated amp. It's a hybrid tube/ss amp that puts out 110 wpc into 8ohm and 220 wpc into 4 ohms. That amp is very musical and I think will make a great match with the Thiel 1.6s. If you have a Pathos dealer near you try to audition it (preferably with your speakers). It's a wonderful amp and should have more than enough juice to drive your 1.6s with ease. Plus the one box solution will help you save on a set of ICs as well. My 2c worth.