I would say the EdgeHD, but honestly, the non-Edge SCT might be a better value unless you plan to do lots of imaging at native focal length. With the non-Edge, there are better reducers out there than the Celestron Edge reducer, and would probably be the best compliment to what you have.
I'm suggesting the SCT because of the versatility of focal lengths that come with the SCT… you can get the hyperstar and image at f/2 around 400mm. This would be a pretty solid focal length when paired with the 2.9 micron pixels of the 585.
Your current scope is around 900mm. If you can get your hands on a starizona night owl .4 SCT reducer, you're around the same focal length but at f/4.
With a starizona .63 reducer, you're imaging around 1400mm at f/6.3ish (I think it's a little higher for the C8), which would be a bit oversampled of course, but provides a nice focal length extension for smaller targets like galaxies and planetary nebulae. You can always bin your camera if you don't want to be oversampled.
You can image at native focal length around 2000mm again for PN or other small objects. Coma and curvature aren't a huge issue if your object is small and centered in the FOV.
You can Barlow the native FL for planetary work. You can reduce the ROI in sharpcap on your 585 and do solid planetary work.
I have also found that the SCT holds collimation very well, even after being taken in and out every night, and even then, I found collimating and SCT to be much simpler than collimating a newt.
The 8” f/4 newt would be a nice, easy transition for you since you're already using a new, and imaging at f/4 around the same focal length would be nice… but it's fundamentally not much different than what you have, so it may not be worth it.
I'll caveat this with the fact that I don't have experience with a RC, but I understand that they can be challenging to get setup and collimate, but once it's set up, it can provide some very nice results. That said, you would be limited to only the longer focal lengths (I think RCs can be slightly reduced and you can always Barlow). So if you're goal is to only use the new scope for galaxies, PN at 1400-1600mm or maybe barlowed planetary work, then this might be a good option, but you lose out on the flexibility fast, wide field optics you could get with the SCT and a hyperstar.
I'm sure you'll be happy with whichever you pick, but I suppose the age old question is: what's you're primary goal for the new scope? What types of targets?