So, I found out today that the beastman cave trigger is actually the cutscene at Uklangor, OR the vine wall. Marmillion will give you the withered vine if you kill Uklangor. I haven't tested this with NOT killing Uklangor but only triggering the scene, although I don't know why you would leave him to have a 2nd cutscene. Its something that can save upwards of 12 steps in the caves, and could require further investigating on what actually triggers what. I tested this with 3 separate game files, 2 with Solo Elf and 1 with Solo Thief. All 3 worked before touching the vines

Note - I did test this on the Bone Flutes in Cave 1 (the passage cave), the Pottery at Cave 7 (Shaman guy), and just entering the main Beastman Cave without fighting anything.

So what about using an Elf instead of FIghter. You get Cleric HD 6-8, still get all the melee weapons, but then can use the Wand of Lightning on a few rooms. Since the wand has limited charges it does add more randomness to a perfect run, but it could save a ton of time in the Trog pile and climbing the Dark Elf realm. It also doesn't clog the screen with animations like spamming the bow does, but you have to be careful of bounceback.

I've been able to use it on the Fire Giant to get the kill. It sometimes takes two shots, its not consistent at all, and ideally you'd need to roll a wand with 4 charges or more (2 for Fire Giant, 1 for Trog Room, 1 for Elf Staircase) Otherwise it should only add 5 seconds to go get it. But it's a speedrun, so random % chance of success can be grinded.

Edit - I now realize that it's only feasible to get the Elf to level 5 by grinding the Fire Giant, as he needs 25000 xp for level 6 and 50000+XP for Level 7. That might not make it viable as the Fighter levels up so much faster and gets a better HP stat

Would the run go faster if you instead used the wand of lightning to kill off your three party members at the start? This way you can use the default characters (saving up to 4 minutes at start of run) And since you can pick up the gauntlets of ogre power in the first tower (still disputed whether it matters), I tried this and I was able to get to the Beastman Caves a lot faster than your run, and I am not optimizing movements yet. I did need to hit the fire giant 1 extra time (when he moved right, i also moved right and shot twice, killing him) I don't have a video yet for this (I just watched your run yesterday) but I'll try to make a video for you