The 13 ohms impedance is a low impedance; the Æons will need to be driven by a headphone output stage capable of delivering enough current into such a load. So you will need a headphone amp with a matching low output impedance.
However, the Æon in practice is not difficult to drive, but you will get best results with an amp with suitable power.
Try the Violectric HPA V200-A (10th Anniversary Edition) or Violectric HPA V280, which are in or near your price range, to see if you like the combo.
If you want to have a headphone amp matching the SQ of your Rossini, I can recommend the Benchmark HPA4, but this one is way out of your price range. However, if possible, try to listen to a Violectric and the Benchmark, and see if you would be willing to pay more, based on the SQ you will experience.