Wanted to build around Aggron, ended up winning a tournament set with it.
Overview
Aggron is an underexplored sweeper in BDSP with rock polish and speed investment allowing it to wipe most of its would-be checks off the face of the map. The combination of thunder-wave and discharge/static from Zapdos slow down offensive threats to the team such as Lati and opposing physical Infernapes to allow Nidoking and our own Infernape to break cores to the point of allowing Aggron to rock polish up and clean with its hard-hitting coverage.
Team Members

: Nidoking is a notoriously difficult mon to switch in on in BDSP. Guessing correctly can either claim KO's or force the opponent to play defensively. This set is standard quadruple special coverage, though 4 Attack naïve nature with focus punch over flame is an acceptable switch to punish Blissey switch-in without doubling to Infernape. It's primary role is to threaten physical walls that might feel safe coming in on Infernape to weaken them for the Aggron sweep.

: A relatively reliable rocker, Blissey may be a momentum loss but stops Alakazam from completely running over the team. Despite being a para spam team this set does not run T-wave but rather healing wish to revive crucial mons depending on the matchup. Most often this is Infernape as it does not appreciate coming in on rocks and killing itself with flare blitzes, though you could just as easily store it for later or revive Nidoking or one of the electric walls, namely the recovery-lacking Rotom-wash.

: One of the most standard pivots in the tier and for good reason. Electric typing with ground immunity serves this team well given the amount of ground-weak mons and lack of fire resist. Thunder-wave is not as common as wisp on defensive washtoms but is a crucial move on this team as rotom so often allows in Latias, giving rotom the ability to slow it down and volt switch out to Blissey before it attacks rather than hard switching and having the opponent predict the incoming Blissey. Protect is an excellent scouting option that also allows rotom to heal from leftovers and stall weather turns. The 8 speed EVs will allow it to outspeed Crawdaunt while investing as much in physical bulk as possible to compensate for the other rocks-weak physical wall on the team.

: While not as common in BDSP as it is in SwSh due to the lack of heavy duty boots, defensive Zapdos is still a reliable pivot and utility mon. A high base speed allows Zapdos to outspeed jolly Breloom with little investment and punish it by threatening to paralyze it with discharge or static contact. Being speedy also allows Zapdos to quickly u-turn out after defogging on switch-ins that Zapdos cannot touch like Gliscor or Blissey.

: You should not bring Aggron out until mid-game at the earliest, but once it is in, and it can set up on a respectable amount of the meta, Aggron instantly becomes very threatening to many teams, even if their checks are still healthy due to its powerful dual stab and earthquake coverage. Usually, you will be setting up on the likes of Clefable, Scizor, Blissey, Azelf, Jirachi, Celebi, and occasionally Latias (especially after it draco's something else) or even Staraptor if it's not locked into Close Combat. 204 speed EVs allows Aggron to outspeed the likes of Alakazam after a rock polish and begin threatening KOs. I'll leave some calcs below.
252+ Atk Life Orb Aggron Head Smash vs. 252 HP / 252+ Def Tangrowth: 192-227 (47.5 - 56.1%) -- 82.8% chance to 2HKO
252+ Atk Life Orb Aggron Head Smash vs. 248 HP / 252+ Def Slowbro: 211-250 (53.6 - 63.6%) -- guaranteed 2HKO
252+ Atk Life Orb Aggron Head Smash vs. 244 HP / 132+ Def Gliscor: 211-250 (59.9 - 71%) -- guaranteed 2HKO after Poison Heal
252+ Atk Life Orb Aggron Head Smash vs. 252 HP / 0 Def Cresselia: 265-313 (59.6 - 70.4%) -- guaranteed 2HKO
252+ Atk Life Orb Aggron Head Smash vs. 248 HP / 252+ Def Rotom-Wash: 214-253 (70.6 - 83.4%) -- guaranteed 2HKO after Leftovers recovery
252+ Atk Life Orb Aggron Head Smash vs. 248 HP / 252+ Def Mew: 224-265 (55.5 - 65.7%) -- guaranteed 2HKO
252+ Atk Life Orb Aggron Heavy Slam (120 BP) vs. 0 HP / 4 Def Latias: 270-320 (89.7 - 106.3%) -- 37.5% chance to OHKO

: Banded Infernape is a great way to gain momentum in a game and keep opponents trapped in volt/turn hell. Banded u-turns, blitzes and close combats primarily weaken checks to Nidoking and Aggron, and punish paralyzed Latias hard. It is also the offensive check for offensive threats to the team like Weavile and Breloom, making it the most common benefactor of Healing Wish. Due to an otherwise general lack of priority and speed on the team without setup, I would not recommend losing mach punch for thunder punch coverage.
Weaknesses

: While Weavile does not want to lock into crash vs. rotom or throat chop vs. zapdos, it still forces an uncomfortable position as rotom lacks recovery and infernape lacks bulk.

: Both faster than every member of the team and able to apply serious pressure, especially with life orb psyshock sets since Blissey will not appreciate this.

: Keep rotom alive. Just keep it alive at all costs.

: While both Infernape and Nidoking outspeed and threaten to KO it, you should be careful to not allow it to come in on the likes of Blissey or Rotom. Zapdos will almost always beat it due to its resistance of both STAB but you will likely have to sac something to spore in order for it to win the 1v1.
TL;DR: spread paralysis, get chip, and don't miss head smash with Aggron.