The 5E mounted combat rules have quite a few incomplete parts that can lead to inconsistencies like this when combined with strict RAW in grid-based play. Similar to gatherer818's answer, my go-to solution is to treat the combined mount/rider as a single Large creature for most targetting, movement and range rules. This also has some bad edge cases for area effects centred on the rider, but those seem less common for mounted combat: In my experience, characters that specialise in mounted combat tend to less access to medium-distance auras/areas of 10 or 15 feet, which is where the obvious power boost for becoming Large would be. The Paladin aura boost I even view as appropriate and thematic.
Using your interpretation of the rider taking a separate space on the mount, it is worth going back to basics and recalling that it is only a convenient representation to make the game playable. Characters don't really take turns in fight, movement is really simultaneous, but initiative and turn-based rules are used to break things down into useful units for the game. Similarly, with the rider position solution you present, the character is not really occupying the right rear flank of a somewhat squarish horse, instead you are using that representation to show "this is where the fight is" around one key character.
Bearing that in mind, you want a simple ruling that matches the narrative of skilled rider maneuvering to protect their mount. I find it reasonable here to temporarily drop worrying about the specific location of the rider, just for this one attack, and allow the re-direct to occur regardless of reach - i.e. the enemy's attack is rolled against the rider ignoring what reach rules would tell you on the map. This patches one annoying issue with the approach of tracking the rider position, which is otherwise sound and fixes some other edge cases.