Jr can indeed rush down that kid, despite him having a juggle-breaking 3 frame NAir and longer-ranging UAir & DAir. There is the question of "Should I feed him Mechakoopas or uncharged Cannonballs?" To that, I say Mechakoopas, because you then unlock the use of charged Cannonballs that can pierce his Lloids, Slingshots, and Trees. However, if you go for this, you better keep a close eye on whether or not Mecha's still Pocketed. You don't want to feed him charged Cannonballs by accident, since it'll KO ridiculously early while piercing Mechas. I've had a buddy Jr in FG Teams lose a stock to this, and I couldn't defend him, due to that Villager's partner succeeding in walling me out long enough to secure that KO. The Villager may also read this game plan by quickly throwing away Mechakoopas (likely onto your squishy face), which will then bar you from freely lobbing charged Cannonballs at him. This can still be an opening for you to get in if you read the Mecha throws.
Side B Jump Cancels will definitely be one of your best friends here, for it'll help you survive the kid's bowling ball edgeguards, as well as his other more active edgeguard attempts. However, you better hope the kid's not above you when you start up Up B, because his DAir & especially his NAir will likely gimp you early, possibly even when mashing the airdodge button to try to get your Car back. On-stage Side B JCs are great for dodging Tree growth & chopdowns, Lloids, and even Slingshots if he's been trained to immediately jump after seeing you JC out of Side B enough times (you can airdodge immediately after JC-ing if he waits for you to JC before Slingshotting).
Against Custom Villager, I'm not entirely sure which deck to take. I'm thinking 3322 or 3122. I'm at least certain that Impatient is the best of the 3 Mechas for this, because of how little gain he gets from Pocketing it (doesn't it explode in his hands within a second or two after bringing it out?). Air Cannon is probably the least self-destructive of the 3 Cannons we can fire at him as well, aside from edgeguarding us.
I want to say that Meteor Ejection will be helpful in surviving his far-out edgeguards and handling his Explosive balloons when we're trying to edgeguard him, but its lack of vertical height is painful for trying to get around his other edgeguards when our super armor's gone, as well as limiting the distance that we can go in edgeguarding him.
I really don't know which Side B to bring. I want to say Grounding Dash to get us through Pushy Lloids, Trip Saplings, and Slingshots, but what would Drift offer us here? Would Side 1 suffice here?
Would Customger swap out Pocket for Garden in response to us repping Impatient & Air Cannon?