I opened this thread thinking your requirements would be more elaborate. There are plenty of ottomans of that size around these parts (Toronto area) and even at the price point you're looking for. Most of the ones with reversible top cushions I know of have the top divided into 3 sections and only the outside two have the flippable cushion. They can't slide off the ottoman when flipped either. If you didn't want reversible cushions, there are a ton of places to get that size ottoman with storage.

My wife and I are looking for something similar, but it has to be bigger. Either a square or a wider rectangle. This is much more difficult to find because they either don't have storage, are very shallow or very expensive (even still missing the other two points).

I'm actually thinking of making my own - which won't be too difficult. I'd then have it custom upholstered, the part I don't have experience with myself.