Even with the ruling for this slate, I'm able to submit a good amount of my ideas. Yay!
Parents: Darmanitan + Weavile
Shared Egg Group: Field
Offspring Name: Darmanivile
New typing: Fire/Dark
New base stats: 97/140/70/47/80/120 (554 BST)
New Ability + description: Sheer Force + Pressure = Brute Power (Basically Sheer Force + Pressure)
Notable moves: Swords Dance, Flare Blitz, Knock Off, Icicle Crash, Poison Jab, Earthquake, Rock Slide, Zen Headbutt, U-turn, Superpower, Fake Out, Ice Shard
Role identification: A massively strong sweeper/late-game cleaner. With an Attack stat equal to that of vanilla Darmanitan, a Speed stat which lets it tie with Arceus, and an excellent STAB combination, Darmanivile will be a destructive force if it gets voted. The main thing it gets that vanilla 'Tan doesn't is Swords Dance, which means that if you have an opportunity to set up, Darmanivile will run right through the opponent's entire team. Darmanivile's main problem, however, is its bulk, as it can barely take non-resisted hits. Use it intelligently, however, and it will not disappoint you.
Parents: Quagsire + Gogoat
Shared Egg Group: Field
Offspring Name: Goatsire
New typing: Water/Grass
New base stats: 119/102/83/91/83/61 (539 BST)
New Ability + description: Water Absorb + Sap Sipper = Sap Absorb (The bearer heals 1/4 of its max HP when hit by Grass moves; Grass immunity)
Notable moves: Recover, Leech Seed, Horn Leech, Scald, Substitute, Bulk Up, Waterfall, Earthquake, Rock Slide, Ice Punch, Leaf Blade, Zen Headbutt
Role identification: A wall with Ludicolo's cool typing, exceptional defenses, and enough Attack to not be set-up fodder. Goatsire's typing in conjunction with its Ability gives it resistances to Ground, Steel, and Water, three common typings in FE, and an immunity to Grass-type moves. Combined with Leech Seed, Leftovers, and no less than three recovery moves, Goatsire can stick around for quite a long time.
Parents: Snorlax + Avalugg
Shared Egg Group: Monster
Offspring Name: Snorlugg
New typing: Normal/Ice
New base stats: 137/123/134/64/88/39 (585 BST)
New Ability + description: Thick Fat + Ice Body = Thick Ice (The bearer takes half damage from Fire moves, and is immune to Ice moves)
Notable moves: Power-Up Punch, Return, Ice Punch, Earthquake, Fire Punch, Thunder Punch, Crunch, Stone Edge, Superpower, Seed Bomb, Gunk Shot, Zen Headbutt, Recover, Curse, Rapid Spin
Role identification: By fusing with Avalugg, Snorlax finally has reliable recovery! It also gets Rapid Spin, which is a neat addition. An Assault Vest set is also on option due to Snorlugg's good special bulk and excellent physical bulk. Thick Ice removes its Fire weakness and makes it an amazing switch-in to Ice-types, but unfortunately does not do anything to cover its other weaknesses to Rock and Fighting, the latter of which is a 4X weakness and the former of which makes it weak to the hazards it is supposed to remove.
Parents: Infernape + Hariyama
Shared Egg Group: Human-Like
Offspring Name: Infernayama
New typing: Fire/Fighting
New base stats: 120/122/75/82/75/89 (563 BST)
New Ability + description: Blaze + Thick Fat = Blazing Fat (Blaze + Thick Fat effects)
Notable moves: Swords Dance, Fake Out, Close Combat, Flare Blitz, Knock Off, the elemental punches, Mach Punch, Stone Edge, U-turn, Poison Jab, Stealth Rock, Slack Off, Will-O-Wisp, Taunt, Substitute, Bulk Up, Belly Drum, Flame Charge
Role identification: While Infernayama will inevitably be compared to Sawkape, it's bulkier in exchange for being slower and slightly physically weaker. That said, it's far bulkier than Infernape and Hariyama appreciates neat options like Stealth Rock, Will-O-Wisp, and Taunt. You can also go down a more offensive route, with sets like Swords Dance, Assault Vest Hariyama 2.0, and even a few Belly Drum sets, but I believe the most popular will be a defensive set with Slack Off, Will-O-Wisp, Stealth Rock, and a STAB move, maybe Fire Punch?
Parents: Vaporeon + Rhyperior
Shared Egg Group: Field
Offspring Name: Vaperior
New typing: Water/Ground
New base stats: 132/112/105/92/85/62 (588 BST)
New Ability + description: Water Absorb + Solid Rock = Water from the Rock (Water Absorb + Solid Rock effects)
Notable moves: Scald, Stealth Rock, Wish, Protect, Earthquake, Rock Polish, Swords Dance, Baton Pass, Heal Bell, Toxic, Haze, Stone Edge, the elemental punches, Iron Head, Poison Jab, Megahorn, Dragon Tail
Role identification: An exceptional defensive Stealth Rock setter. Having semi-reliable recovery in WishTect allows it to set up Stealth Rock multiple times, if needed. 132/105 physical bulk means that Vaperior can take hits from all but the strongest physical attackers. The Solid Rock half of the Ability doesn't do too much, but it could potentially help Vaperior survive a Grass attack aimed at it.
Parents: Torterra + Lilligant
Shared Egg Group: Grass
Offspring Name: Lilliterra
New typing: Grass/Ground
New base stats: 92/94/100/102/90/83 (561 BST)
New Ability + description: Overgrow + Own Tempo = Tempo Growth (If the bearer is confused, it snaps out of its confusion and gets a 1.5x boost to its Grass moves; these boosts don't stack)
Notable moves: Quiver Dance, Petal Dance, Earth Power, Giga Drain, Hidden Power, Sleep Powder, Swords Dance, Rock Polish, Wood Hammer, Earthquake, Stone Edge, Superpower, Crunch, Petal Blizzard, Stealth Rock, Synthesis, Healing Wish
Role identification: Quiver Dance and Petal Dance is a no-brainer with Lilliterra's Ability, but it's versatile enough to use a double dance set with Swords Dance and Rock Polish. It can also use Stealth Rock if it really wants to, and has Sleep Powder and Healing Wish for team support.