I know you said no repeats, but its a bit unclear which type you want to take precedence if a Pokemon has the highest base stat total for both of its types, so I'm just going to list the top 3 (sometimes 4 if there was a tie) for each type for simplicity
Normal: Arceus (720), Slaking (670), Regigigas (670)
Fire: Primal Groudon (770), Arceus-Fire (720), Ho-Oh (680), Reshiram (680)
Water: Primal Kyogre (770), Arceus-Water (720), Palkia (680)
Electric: Arceus-Electric (720), Zekrom (680), Mega Ampharos (610)
Grass: Arceus-Grass (720), Mega Sceptile (630), Mega Venusaur (625)
Ice: Arceus-Ice (720), Kyruem Black (700), Kyurem White (700)
Fighting: Mega Mewtwo X (780), Arceus-Fighting (720), Zamazenta (Crowned Shield) (720)
Ground: Primal Groudon (770), Arceus-Ground (720), Zygarde Complete Forme (708)
Poison: Eternamax Eternatus (1125), Arceus-Poison (720), Eternatus (690)
Flying: Mega Rayquaza (780), Arceus-Flying (720), Mega Salamence (700)
Psychic: Mega Mewtwo Y (780), Mega Mewtwo X (780), Ultra Necrozma (754)
Bug: Arceus-Bug (720), Mega Pinsir (600), Mega Scizor (600), Mega Heracross (600)
Rock: Arceus-Rock (720), Mega Tyranitar (700), Mega Diancie (700)
Ghost: Arceus-Ghost (720), Giratina (680), Lunala (680), Dusk Wings Necrozma (680)
Dragon: Eternamax Eternatus (1125), Mega Rayquaza (780), Ultra Necrozma (754)
Dark: Arceus-Dark (720), Mega Tyranitar (700), Yveltal (680), Hoopa Unbound (680)
Steel: Arceus-Steel (720), Zacian (Crowned Sword) (720), Zamazenta (Crowned Shield) (720)
Fairy: Arceus-Fairy (720), Zacian (Crowned Sword) (720), Mega Diancie (700)
Source
Hope this helped!