It doesn’t seem like the Hat contains parts of the Founders’ souls.
The only mention in the books on how the Sorting Hat got its abilities is in one of its songs. The Hat says the Founders “put some brains in”, which seems to imply some kind of enchantment rather than them putting their soul off.
“While still alive they did divide
Their favourites from the throng,
Yet how to pick the worthy ones
When they were dead and gone?”
Twas Gryffindor who found the way,
He whipped me off his head
The founders put some brains in me
So I could choose instead!
Now slip me snug about your ears,
I’ve never yet been wrong,
I’ll have a look inside your mind
And tell where you belong!”
- Harry Potter and the Goblet of Fire, Chapter 12 (The Triwizard Tournament)
In the Pottermore writing by JKR on the Sorting Hat, again the idea of the Founders putting their intelligence into the Hat is referenced. The Hat is also referred to as one of the cleverest enchanted objects most wizards will ever encounter.
Legend has it that the hat once belonged to one of the four founders, Godric Gryffindor, and that it was jointly enchanted by all four founders to ensure that students would be sorted into their eponymous houses, which would be selected according to each founder's particular preferences in students.
The Sorting Hat is one of the cleverest enchanted objects most witches and wizards will ever meet. It literally contains the intelligence of the four founders, can speak (through a rip near its brim) and is skilled at Legilimency, which enables it to look into the wearer's head and divine his or her capabilities or mood. It can even respond to the thoughts of the wearer.
The Sorting Hat - Pottermore
It seems to work more like the portraits of the Headmasters.
The portraits of the Headmasters at Hogwarts seem to work in a similar way, retaining the behavior and personality of the people depicted in them. The Pottermore writing by JKR on the Hogwarts portraits explains how they get their knowledge. The Headmasters teach their portraits the knowledge of them that they want them to have, and this knowledge lasts through the centuries. The Founders could have done something similar with the Sorting Hat - it would be consistent with what was said about the Hat’s intelligence.
Some magical portraits are capable of considerably more interaction with the living world. Traditionally, a headmaster or headmistress is painted before their death. Once the portrait is completed, the headmaster or headmistress in question keeps it under lock and key, regularly visiting it in its cupboard (if so desired) to teach it to act and behave exactly like themselves, and imparting all kinds of useful memories and pieces of knowledge that may then be shared through the centuries with their successors in office.
Hogwarts Portraits - Pottermore
It’s unlikely there’s a not-Dark way to split the soul.
Slughorn defines a Horcrux as any object that conceals a part of a wizard’s soul. The act of splitting the soul is described as inherently evil. It’s made clear that the soul is supposed to remain intact, and that splitting it is “wrong”.
“How do you split your soul?’
‘Well,’ said Slughorn uncomfortably, ‘you must understand that the soul is supposed to remain intact and whole. Splitting it is an act of violation, it is against nature.’
‘But how do you do it?’
‘By an act of evil – the supreme act of evil. By committing murder. Killing rips the soul apart. The wizard intent upon creating a Horcrux would use the damage to his advantage: he would encase the torn portion –’
‘Encase? But how –?”
- Harry Potter and the Half-Blood Prince, Chapter 23 (Horcruxes)
Because of this, it’s highly unlikely that there’s a way to split the soul using love, or any other form of neutral or “good” magic.