The setup should have worked well in theory, but only under the most ideal circumstances, where the client adapters handle roaming properly and/or the client is in an area where it cannot even hold a reliable connection with one of the routers. The problem you're having is that the adapters don't know when to switch, because there is enough overlap in the signals of the two routers that the client sees no reason to switch, because the one it's on is still sending and receiving packets. As we said, the clients aren't looking for the best signal, only the one that's serviceable.

Think of it this way: Let's say you have 4 SSIDs (which is what you want to avoid I know). You want to use your tablet. This tablet has connected to all four of those SSIDs at some point and remembers them (and can therefore connect to them automatically). You start off by connecting to the 5Ghz band on your ASUS, the router nearest to you at the time. Then you move to a part of the house where the Asus 2.4Ghz would provide higher throughput because it's capable of longer ranges, and in this area of the house, you can tell your internet is slowing down. Then you go upstairs to sit 3 feet away from your Netgear. Your connection is now slow as hell, and you don't know why. You check to see what SSID you're connected to. It's the ASUS 5GHz, and has been the entire time. That's because you never got fully out of range to the point that your client would drop the connection and automatically connect to one of the other 3 SSIDs it remembers. Even with a unified SSID, most (if not all) of your clients are behaving this way, always prioritizing its most recently connected channel. The client adapter algorithm is not running speed tests, measuring packet rates, or even paying attention to throughput to a certain extent; it's simply scanning for available channels and saying, "this is the most recent one I connected to, and I see it, so I'm gonna connect to it."

If splitting the SSIDs by band allows all your devices to get seamless, reliable coverage, you have your solution. If you're still seeing degrading throughput/coverage when you move from one part of the house to another with the same device, you now know why. The solution is splitting SSIDs by both router and band.

Also, how big is your house? In a lot of cases, a single well-placed router can be the simplest solution. Last year, my dad asked me to help him get full coverage in his house with a Linksys EA4500 (dual band N900). His house is 6000 Sq ft (my parents are retired and living the OT Baller life). It has three floors, and a separate poolhouse area. There's a staircase that starts in a center spot of the house, and if you look up from the bottom of the stairs, you can see the ceiling of the second floor. It was the perfect spot. I demonstrated its awesomeness. Only spotty area was the poolhouse, which could've been solved with an AP mounted by a pool-facing window of the second floor. But nope, didn't want a router on the ceiling. Ultimately, it was the only spot that had full reliable coverage in the main house, so now he's got the house wired like an office building with Cat6, and a couple of APs positioned in various parts of the house.