Rods are kind of a personal thing. We all have our own somewhat unique way of holding and handling them and we have little quirks about us, and while we are pretty similar, we are unique.
There are countless rods made that would be a great match for that reel, but the 'real' question is whether or not they are a great match for you.
So many times I have convinced myself that a certain rod would be awesome for me only to find that when I actually put hands on it, that it didn't suit me well for one reason or another. Or there was another rod I hadn't strongly considered that actually felt better in my hands (and with 'the' reel attached that it would be used with).
These days, I try to either bring my own reels, or use reels the shop has on hand to get a feel for a rod. I usually try several and go back and forth, some hand-wringing, some pacing, etc.. I am probably a bit of a PITA for the shop, but I usually try to bring them my business when possible because I view that as a service they provide that probably saves me money and time since I will make fewer regretful purchases.
For me personally, I like cork. EVA often feels weird and the tactile feel doesn't appeal to me. EVA sections are often on the skinny side and I have. . . big hands. Skinny doesn't feel good to me.
I prefer full cork on casting rods, but it isn't necessarily a deal breaker to quite the extent that EVA has become for me.
Proprietary reel seats can be amazing. Amazingly good or amazingly bad as well.
With all of that said (sorry, not sorry), my best guess is that you would probably be looking for a rod that is around a similar price point at your SLX XT reel (somewhere between $100 and maybe $175)?
If that budget range is in your wheelhouse, I like offerings like the Daiwa Tatula (or Kage) 7'3" MH/F. You can have mine when you can pry it from my cold dead fingers. You might hate them, and that's fine. For some matching a Daiwa rod with a Shimano reel is borderline blasphemous, but that gene is not dominant for me. But I would suggest checking them out if that is within your budget range and you are able to wear Nike shorts with Adidas shoes without developing an eye twitch.