If anyone had them, it'd probably be
Howard Sams. You might need to track down chassis number info, as you did for the other Odyssey systems (
this YouTube video mentions the number 3616R061A in the description, though I dunno if it's a chassis number, serial number, or what), and the TV and game portions may have separate manuals.
This site claims to have downloads of the owners manuals (two different versions, for some reason) available, but they want $29.95 for them, and I have no real idea of the relevancy (Philips/Magnavox made several TVs with '4305' as part of the model number over the years).
Pong-Story mentions that the circuitry inside is equivalent to the Odyssey 300, though the 4305 pictures and videos I've seen show a color screen, so they may have used a different GI Pong chip like the AY-3-8512.
This site mentions that the 4305 may have had a European equivalent as the "Philips Philetta 405", so that's an additional keyword you could use. Good luck!
-Adam