A few random comments.
I've run my Omegas with:
Musical Fidelity M3i
Various TPA 3116/3110 Class D amps
Rega Brio R
Decware Mini Torii
By far, the SE84 is the best of the lot. The little Audioengine amp is almost really good. Tonally it works better than I think any solid state amp I've tried with the Omegas but it completely falls apart for me in its soundstaging and imaging capablities where it is actually probably the worst of all the amps I've played the Omegas on. Imaging is vague outside of the center image and the outer dimensions of the soundstage just collapse noticeably compared to other amps.
I actually never would have tried the Audioengine amp on the Omegas if I hadn't read Canada Robs recommendation. I've had that amp for a few years running the TV system in my bedroom and had tried it in the past with some conventional speakers where it sounded pretty mediocre at best. When I had first read Canada Robs recommendation I thought "no way" based on my experience with that amp on other speakers, but I tried it on the Omegas and again, tonally it really shined. I was very surprised. If you don't have your system set up for or aren't really into soundstaging and imaging, it's a great match for the Omegas.
The little TPA amps are fun and for the price, outstanding values. For me, the 3116 outperforms the 3110 which sounds a little dead in comparison.
The Brio R is a fun amp with the Omegas. It doesn't have the magic that the Decware amps have though, but there is a nice excitement to the sound it provides.
Besides the Brio, the best of the solid state amps overall that I've used on the Omegas was the Musical Fidelity, but when you can get an SE84 that's so much better for almost half the cost, why even recommend it right? Once you hear the RS5 with a decent tube amp, you'll think "why bother" with solid state. That said, I've toyed with the idea of getting a First Watt for a few months now. I know Nelson Pass has used them on Omegas himself and he uses single driver speakers when he voices those amps.