I am driving my Tyler Taylo Reference Monitors with a YBA Passion Integre 100 and couldn't be happier. Your Linbrooks are a bit different than the Taylo but would most likely do great with the YBA line. A used YBA Passion Integre is still a bit out of your budget, if you could find an older Integre DT (pre Passion series), I think you'd be very happy. I have no doubt the YBA can get the most out of your Linbrooks. I am continually amazed at how well the YBA drives my Tyler speakers. Do some research on the YBA line. The Audio Refinement Complete line was built by YBA as their "budget" series and has been replaced by the YBA YA-201 integrated, which is in your budget. Personally, I'd wait for an Integre DT to come up, they will probably be in the mid to top end of your budget. If you find one, act fast because they usually go fast. YBA makes some incredibly musical components. I highly recommend you give it a try.
Good luck, Robert