Comparisons

Sun (+itotaka's route, n3ds) vs. Moon (+Keizaron's route, o3ds) Comparison

Assume turns are 6 seconds (they're roughly around that time)

Silk Scarf and Echoed Voice:
No Silk Scarf vs Silk Scarf - ~9 seconds in favour of no scarf
No Echoed Voice vs Echoed Voice - ~45 seconds in favour of no EV + repel + scarf equip
Verdict: Skipping both is faster by ~53 seconds

Ilima fight:
Torrent Water Gun is a range on Smeargle unless 18 IV +Sp.Att nature; Echoed Voice (third tier) is guaranteed on 10 IV -Sp.Att and above
Verdict: Echoed Voice is way safer but not necessarily faster

Berry tree Team Skull Grunt:
X Sp.Att + Water Gun x2 - ~44.5 seconds
Echoed Voice x3 - ~46.5 seconds
Verdict: Assuming Echoed Voice x3 is actually faster, but n3ds vs o3ds loading may be why Echoed Voice x3 is slower; unsure

Rattata/Yungoos:
Can outspeed Yungoos, looks like Yungoos doesn't hurt as much?  Unsure
1/2 turn saved per fight in Sun
Raticate/Gumshoos:
Can outspeed Gumshoos, both appear to be 3 to 4 turn fights depending on rolls
1/2 turn saved assuming equal turns in Sun
Echoed Voice would guarantee a 3 turn fight on Gumshoos
Verdict: Oos are faster than Rats by about 1 1/2 turns

Popplio vs Brionne:
x turns (can be as quick as 2-3) to lose to Hau 3 vs 5 turns to win - 2-3 turns in favour of losing in best case scenario
Skipping Growlithe vs fighting Growlithe - 2 turns in favour of skipping
8 turn Hala 1 vs 7 turn Hala 1 - 1 turn in favour of early Brionne + time to equip Oran Berry (negligible)
Verdict: 3-4 turns faster to stay as Popplio in best case scenario, but riskier

Dexio vs Sina
Echoed Voice Dexio: 3 turns on Slowpoke, 2-5 turns on Espeon (wildly inconsistent depending on Sp.Def, damage taken and broken voice chain) - 5-8 turns
No Echoed Voice Dexio: 5 turns on Slowpoke, 2-3 turns on Espeon - 7-8 turns
Echoed Voice Sina: 2-3 turns on Delibird, 2 turns on Glaceon - 4-5 turns
No Echoed Voice Sina: X Sp.Att x2, 1 turn on Delibird, 2-3 turns on Glaceon (very favourable 2 turn) - 5-6 turns
Verdict: Moon is faster and more consistent than Sun; Echoed Voice can save a turn in Moon and potentially two turns in Sun

Hau 4:
Losing: 2-4 turns
Winning: 4-6 turns, depending on damage taken
Verdict: Losing is faster, duh.

Gladion 1:
Echoed Voice: 2-3 turns on Zubat, 1-2 turns on Type: Null - 4-5 turns
No Echoed Voice: 4 turns on Zubat, 2 turns on Type: Null - 6 turns
Verdict: Echoed Voice saves 1-2 turns

Wishiwashi (assuming no Alomomola):
Echoed Voice: 4 turns
No Echoed Voice: 5 turns
Verdict: Echoed Voice saves 1 turn

Hidden Power takes about 30 seconds to get and teach and saves about 24 seconds potentially with a super effective move against grass

Solgaleo is taught 2 moves instead of 1.

Gladion 3:
Solgaleo - 6 turns
Lunala - 7-8 turns (one Z move)
Verdict: Solgaleo is faster by 1-2 turns plus no Z move

Hau 6:
Solgaleo (+ Primarina) - 8 turns + changing to Switch style + two "switch" text boxes + two swaps
Lunala - 8-9 turns (one Z move)
Verdict: Solgaleo is faster only because of the Z move

Hala 2:
Solgaleo - 6 turns
Primarina - 7 turns (plus swap to front)
Verdict: Solgaleo is faster by 1 turn

Olivia 2:
Solgaleo - 10 turns (Elixir was used when Carbink was sent out)
Lunala - 9-10 turns
Verdict: Solgaleo is slightly faster (Lunala has to be switched back to the front)

Acerola:
Solgaleo - 9-11 turns (dependent on Shadow Claw crits and health for Aftermath)
Lunala - 9-11 turns (dependent on Shadow Ball drops and healing)
Verdict: Solgaleo is most likely faster; no healing before fight is needed like Lunala

Kahili:
Solgaleo - 8 turns
Primarina - 9-11 turns (plus swapping to front)
Verdict: Solgaleo is faster

Kukui:
Solgaleo - 14 turns (more if more heals are needed)
Primarina + Lunala - 14-17 turns (dependent on Primarina succeeding or failing)
Verdict: Solgaleo is faster on account of Primarina faint + Lunala swap