Biggest time gain is from after Morty. 
In the new route, you Bike down to New Bark and get and equip the Magnet. 
In the Old Route you get Fly (Beating Chuck), Charge Beam, and Hidden Power, teaching all 3. Also Strength, which you now get before Morty.
In Old route you also take Goldenrod Mart after Morty, buying Thunder, and x items, where in New route you take Celadon Mart.
In both you get a Rare Candy (LoR vs Violet Candy. Can also do triple tweak candy instead of Violet, would save an additional ??? seconds)

Timing, Start: After warping from Morty's tile | End: Exit menu before New Bark Tweak
Old Route: 11:58 (Includes 3 cutscenes that are accounted for afterwards in Strength/Boaba/Rival)
New Route: 2:47 [Includes teaching Shadow Ball, Strength, Surf]

Time Save: 9:11

Other movement/menus:

Time gain:
No Kenya (12.8+9.2) = 22 sec
E4 Mart (no gathering/selling): (4.5 + 8.9 + 4.9) = 18.2 sec [Assumes buy 2 items, e.g. Fullies and Hyper]

Total: 40.2 sec

Time loss:
Get Charcoal = 44 sec
Longer Goldenrod Mart 1 (more buying/selling): (17.5 + 4.9 + 4.9) = 27.3 sec
Level 24 on Quilava = 8.1 sec
Bike to Strength after Koffing = 30.5 sec
New Bark -> Olivine (includes Boaba/Rival Cutscene) (2:08 + 22.5 + 19 - 18) = 2:31.5
Run to Vermillion (18.9 - 15) = 3.9 sec
Take Celadon Mart (Max Repels, no healing items) = 1:57.2 
Pallet -> Mt Silver (39 - 19) = 20 sec


Total: 6:42.5
Net total: 6:02.3


Battles: Everything before the last 3 (Lance/Blue/Red) is fairly negateable in that it's almost even with some on each side. It's probably actually a bit better in the new route if everything goes as planned, but a touch riskier.

Time gain:
Whitney (~0.8 turns) | No Speedtie on Miltank
Fairy Doubles (~idk) | Old: 1:37.8, includes Super in fight
Rival 3 (~0.2 turns)| Lvl 23 for Croc means X Spec before second hit, can save time with burn/blaze
Morty (~0.01 turns) | Thunder vs old Spark almost identical
Can Thunder Flareon
Spark 100% on Golduck/Vaporeon
Can SB (SB) Flaaffy
Rival 4 (~0.4 turns) | No X Spec, but a 3rd thunder (skip 2 CBs) and 5/8 range on Golbat, and 7/16 range on Magneton

Time loss:
SB Range on Victreebel instead of HP 
Thunder range/SB + SB on Parasect
Karen: (~0.5 turns) | Skip Charge Beam luck, but have to SB + SB Vileplume

Real Time loss: 
Lance: (~3 turns) | More setup.
Blue (Overall manip) [Roughly 15 seconds]
Red (Overall manip) [Roughly 15 seconds]

Time loss: ~55 sec

Other:

Manip is also slightly different to start, but unsure on time diff. Prob lose a tiny bit of time, just based on location manip being worse than anything else, but also things like manipping pokerus, which is a couple extra seconds of running around.

Estimate loss: 14 seconds

Time save: 9:11
Time loss: 6:02 + 55 + 14 = 7:11

Total time save: 2:00 (Estimate)

Note: This is compared to the newest route before this re-route. Compared to my PB it saves even more time, as my PB did not have updates from in between, such as extended manip after Falkner (saves using repels, time+money), and didn't do RNG Manip against Blue at all.