Round is a tricky cut, especially for shorter cooking times. I know people use it for "steak" cooking methods, but I've never loved it. It's in the rump of the cow, and so see a lot of work. Leaving it with nice beefy flavor, but in a cut that is lean and tough.
Tough is bad for short cooking times because it comes out chewy. Slicing and pounding does do a little to offset this, but in my opinion, not enough.
Lean is bad for long cooking methods because it comes out stringy. I don't love this cut in things like stews and chilis because it can be fibrous and you tend to spend a lot of time picking it out of your teeth.
Some more ideal ways to eat this cut are less traditional, but some of my favorites. It is great in steak tar tare, cut or ground into tiny pieces. It is also yummy when slow braised in a big piece, and then sliced thin once its allowed to cool, and reheated in the braising liquid. While you might not have this method at your disposal, it would be good cooked at a low temperature with an immersion circulator for a long time and then sliced. (Most know this as "sous vide" - but that term, translating literally to under vacuum, actually infers that you're using a vacuum sealer. The term "low-temp cooking" is a little more accurate.