I may be wrong but you shouldn't lose that many frames, even without the boomerang. The only place I could see you losing this many frames, is the room with the rat and the key (still in Hyrule Castle) For the blue knight and the mini boss, you can hit your target towards the door/cell and should lose no more than 15 frames to collect the keys. For the Eastern Palace, an educated guess says that you should lose no more than 30 frames, and this is in the dark room with the key under a pot.
You should be able to collect rupees/arrows from the following things without any time loss:
Octorok at the Statue you need to wait for (since you don't have the boomerang, manipulate it to be in front of you so you can collect it on your way through)
Skeleton room: kill both skeletons and make sure they drop items, don't worry about picking them up.
Two rooms before the Big Key, there is a monster you must kill to reach the switch, make sure this drops something. On your way back, you should consider going up instead of down, since you don't have the boomerang to collect the rupee from the second monster, though I'm not sure if you can pass those spinning fire things.
OPTIONAL: In the second dark room, since you don't have the boomerang, use the pot you just picked up and kill a skeleton as you're waiting to pick up the key.
Big Key room, throw the pot against the monster to make it drop a rupee (be it blue or red depending on what you did two rooms back)
Room after Bow, you should make as many monsters drop rupees as possible. If you didn't get a red in the big key room, get it here, as well as a blue. Killing the second cyclops is the best option as you need to wait for the key to drop, though picking up the arrows is entirely optional. You should have enough arrows regardless, for the upcoming boss and the Llanmolas.
Note: there is a room to the right which holds 100 rupees on the ground. Since you need a lot more of rupees than I do, consider this room, but personally, I think this room isn't worth it.
Two rooms before the boss, there are two skeletons. Depending on if you did the OPTIONAL I said earlier, kill the skeletons in an appropriate order so that you will get the arrow drop.
Final room: try to get at least another red rupee here.
Now that I've thought deeply into a run without the boomerang for half the way, you don't lose as much time as I've expected. Though, I do see a few seconds lost in the Tower of Hera and Hyrule Castle part 2, but that would be it, until the end of Thieves' Hideout.
Also, thanks for fragitious for bringing this up earlier. I have small doubt that the magic boomerang chest you will get, is the only chest of it's kind. You should do some exploring to see if there are any other chests that may give also give a magic boomerang.
