My suggestion is, stay away from integrated amp with build in DAC. They typically use a low to lower mid grade DAC chip. People say it is implementation that matters most... True, but I would go with one that is well implemented but based on a chip that is no more than 2 steps from a flag ship DAC chip.
If you don't mind used, you should be able to get the excellent NAD C356Bee that has been discontinued, or even the C275BEE for under $1,000. There are plenty of external DACs in the $200 price point that are far superior than those build in ones, albeit one can argue that the difference in specs and measurements may not result in audible difference.
If you are serious about saving money though, then bite the bullet and grab a $500-$600 AV receiver such as the AVR-X3500H. You would have to pretend it is a two channel stereo receiver. It will outperform the Sprout for sure.
The Elac will likely have more accurate/balanced sound quality, but the RTiA7 can play much louder so it should be an easy decision for you, if based on your need.