Huh...I didn't think of that. Well, let's see how it stacks up.
Getting rupees wouldn't take too much time, as we'd nicely pass the Zora Pots game on the way to the fountain, immediately paying for the bombchus used to hover. Of course, we lose 2 warps (1 into Ikana and 1 back into the Great Bay) and the time it takes to get from the GBT owl statue to Ikana, plus the time it takes to do that stuff in Ikana (probably :30). So I'm estimating time loss of about 3:30.
Going to Ikana takes a good 2:00 at least, and going to the swamp is about 1:30. So we're about even here. However, we also save 10 bombchus by not hovering over the skull kid cutscene. Also, the above times were gathered from Mukki's run, which had the Goron Mask, which made these particular areas faster. Using this alternate route, we get...
First cycle stuff (220r)
Buy bomb bag +20c (20c) (90r)
Get into North Bay (19c)
Get Zora Mask, hit Owl statue, go to South Bay
Zora Pot game, Song of Double Time (180r)
Go to Fairy Fountain
Hover to Ikana (4c)
Hit Ikana owl, go to witches' hut
Get bottle
Kill Big Octos with Zora boomerangs
Get Sonata
Get Song of Soaring
Get Bow (0c)
Warp out to CT
Buy 10c, head to Ranch (10c) (140r)
Get Ranch Bottle (6c)
*Song of Double Time when dawn comes*
Warp to North Bay
Get Hookshot+2 Zora Eggs (2c)
Warp back and deposit them at the laboratory
Go back for the other 2 Zora eggs (240r) (0c)
Warp back to CT
Buy 20c more (160r) (20c)
Warp to Woodfall
Wrong Warp to Snowhead (5c)
Complete Snowhead
Warp to CT, buy 20c more (80r)
Warp to Ikana, climb Stone Tower
Warp to CT, buy 20c more (0r)
Warp to Stone Tower, complete temple, get a lot of rupees while in there
*Warp to CT, buy 20c more*
Warp to Woodfall, complete temple
Warp to CT, buy 20c more, Warp to North Bay
Do Pinnacle Rock
Get NWBN
Go to South Bay
Do GBT
Back to CT, Moon
starred line depends on whether we do the Woodfall boss key skip or not, and thus determines how many rupees to get in STT.
So, if 220r is significantly faster than 270r in the first cycle, perhaps we should use this? Ugh, I hate trying to figure out whether massively different routes that differ by seconds in total time are faster or not.
The second Song of Double Time could be held off to immediately after night of the second day or immediately after dawn of the third day. It's best to play it in a place where the "dawn/night of the x day" message doesn't cause a cutscene.
EDIT: As ZFG so kindly reminded me, since we have the Zora mask, we can just boomerang the Big Octos.