The intent is no. The spells that give you extra smite attacks (Twin, Repeat, Extend, Persistent, etc.) aren't supposed to apply each other to your subsequent bonus smites, just the spells that give bonus effects to your smites (Entangling, Empowered, Energized, etc.). Although thinking about it again, even that might not be a great idea. You can just cast the spells before your bonus smites in the later rounds if you want more damage or extra effects. It'll be a lot simpler to write that way. No fancy interactions to worry about, just things that make later attacks also count as smites, and things that add effects to smites. Also no need to worry about unintended multiplication of power, such as a Persistent Reckoning Seeking Smite turning every attack into an auto-hit SoD. For example, you could smite someone with Repeating Smite on one round, and then cast Entangling Smite on the next round and it would apply to the bonus smite from last round's repeat.