You wouldn't have to push bokoblins; I think it's faster to just get slingshot if you're already getting rod.
And yeah, it would be several minutes slower, but still faster than not doing fixed EMS (you said it saves 12 and a half minutes).
-BIT-
1:45 from control of Link, BIT, Talo's play sword text
-No BIT, fishing rod obtained, getting water bombs to enter Lakebed-
7:50 from control of Link, 1st goat herd, fishing rod, catch 2 fish, buy slingshot, exit ordon village, Talo's play sword text
4:00 roll from kakariko village to bottom of death mountain, climb to goron, get knocked off by goron, tame epona, ride to ordon village (not counting Bo fight, since it's done in BIT as well)
2:40 warp to kakariko village, ride epona to grotto, dig, catch 2 bombfish, exit
total = 14:30
Using water bombs to enter lakebed in lanayru twilight takes 12:45 longer than pillar clip. It is even a little slower than BIT (no fixed ems route).
Yeah, pillar clip is very annoying. But you can fail it like 6 times, have a 10 bomb morpheel fight, and it would still be faster than BIT (no fixed ems) route.