I managed to beat the Spirit Temple, and I can confirm that you do not need bombchus to beat it - you can blow up the crack in the wall if you throw a bomb at it.
But I'm at an impasse. How do I get to the Fire Temple without getting the Goron Tunic? Darunia's son controls access to the door to Darunia's room, but if you talk to him he gives you the tunic!
EDIT: Okay, so I talked to his son and then Like Like'd the tunic away, but now that I'm actually in the Fire Temple... welp. Sadly, the timer pause trick isn't to backflip, but to press the ocarina button while backflipping or sidehopping (beats me why), which isn't exactly an easy trick (mistime it and you pull out the ocarina) and I'm not convinced it actually saves you any time over long distances compared to backwalking, especially if you mess up the trick a lot. On top of that, as opposed to the water timer which loved to reset, the fire timer hates resetting and does not reset if you walk between two timer rooms. On top of that, Navi's warning is only a couple of seconds long (if that) compared to the five second warning you got for the water timer.
So, somehow, in twenty-six seconds or so I need to run along the bridge (including jumping over the hole in the middle), go into the next room, hookshot up the railing (luckily the timer pauses while the hookshot drags you around), push the block down, ride it up to the top and pray that the next room isn't also a timer room. I can't even push the block down in time. Does anyone have any advice or past experience?
EDIT2: Well, sorry to disappoint everybody but I'm going to use the goron tunic. I've done some research and basically with superhuman reflexes it's possible to get past this little bit and Volvagia is also possible. However, the Fire Trial... I'm pretty sure it's going to be impossible in the time limit. If I were to use a fairy, I'm pretty sure I could pull all three of these off, but I said at the beginning of this run I wasn't going to use bottles unless absolutely necessary and I'm sticking to that. I'll make a copy of my save file in case somebody comes and proves me wrong, but until then, I'm using the tunic. I'm pretty disappointed, but what can you do.