I haven't figured out how to sneak with the inventory open, and you can't throw berries from the hotbar. I do just throw a stack though. It takes a few days for berries to despawn even outside of workbench range. If your single berry despawns sooner it's because they're eating them. Though it might be helpful to toss out two or three small stacks to account for them wandering a little.

Literally just hide inside a shrub and throw a berry, the Lox aren't hostile they are just easily frightened. Bring some wood and put a work bench inside a safety box of stake walls with a roof the Lox won't react to you building if done behind them.

Only when breaking stacks does one's character stand up when in the crouch position. If you break your stacks up prior to throwing them you will remain in the crouch position. I generally make sure I have 3 cloudberries for each lox I am taming. If I come across a group of 3 lox, I will make 3 stacks of 9 prior to approaching them. This way one's character will not stand after throwing the cloudberries. I will then approach them crouched, with no weapons equipped, and throw my 3 stacks of 9 cloudberries around the cabinet of lox in such a way that I am pretty sure even if they wander slightly, there will be cloudberries within detection range, should they get hungry. I will then move off, making sure I am at least close enough to be able to see the acclimation heart emotes. I usually fish while I am waiting ...

There's no need to break down a stack of cloud berries into single items for taming.
Just throw the entire stack at them and wait. They will eat from it when they are hungry, so it doesn't matter if it's a stack or a single item.

But more to your advantage, throwing a stack at them also means you won't get up more often, thus less chance to startle them in the first place.

From the wiki:

Notes
Creatures only eat one item from stacks so the food doesn't have to be thrown one by one. Player base structures can be used to prevent the food from despawning.

https://valheim.fandom.com/wiki/Taming

Thorin :)

Oh yes there is need to break up the stacks. Usually I sneak up from behind them to throw the berries. I don't get too close so my berries land behind the lox. This causes few things;
1) the lox turns after there is berries available behind it
2) the lox sees/hears me and comes to investigate
3) the berries are left at the ground
4) I hurry to high ground with the lox in tow
5) the berries eventually despawn
6) keep dropping those berries one by one until tamed
7) currently sitting 4th night in a row on top of rock, taming 3rd lox
In any case this is how I manage to tame the beasts but what about the bug/feature, does the same thing happen to you?