Ah, I wondered if you would create this, I was tempted to myself. Luckily though you can be more coherent than I.
Anyway, I like the 'Claiming the Soul' section. Note that souls could be used as political leverage. Nobler succubi have areas of influence probably, areas of hell they have more of a domain over. Hell is probably an infinitely wide dimensional plane, so supporting this is feasible. Though we shouldn't try to formulate succubi culture around making deals, as it's probably more accurately the opposite: deals stem from succubi culture. So as we aim to explain and expand on this, that might be something kept in mind.
Anyway, when it comes to an aristocrat Succubus, if they notice one guy has a contract with a succubus of a lower class, they wont be too afraid of letting the guy have multiple contracts. However, if a noble succubus sees a guy has a contract with another noble succubus, they'll be hesitant, because it means war between them both probably. Also, they might try to do it anyway to undermine another succubi's influence. They could use the guy as a double agent, giving him more power to reward him for services that benefit that particular succubus.
That being said, the contract is special. It's magical in nature, binds a soul in return for power from one side to another (typically). So a contract like this typically has a ritual. You don't just open the book of "thaumaturgy for starters" and read the bold text. Hell isn't that easy to contact, there would be certain things you have to chant, probably, also put a certain combination of things together. Maybe a runic circle, some objects that represent you deep down maybe, just symbolic ingredients in general, ones that this contract would require. The contract offer would probably be like one phone ringing in an open room full of people. The first person to get the phone wins.
In return, the magic from the ritual engages the creation of the contract - and being a contract that can enforce a soul in exchange for power would already have magical properties, but the whole point of this is to support the fact that it may not just be "soul for power". In a contract there are always terms of agreement, small writing, specific, like that bill you vote for with all the tiny writing. You go online to figure out what all the tiny little writing actually means, because read straight through you would probably miss the implications unless your mind is politically geared. The more specific the terms of the contract, the more power or more efficiently power can be transferred to the user.
There's a problem though. The succubus' power is being used by a mortal, that there is the weakness. Succubi already get access to a lot of souls in the first place, giving your power in exchange for rich food is like ripping your fingernail off to get a piece of Buche de Noel. However that Buche de Noel needs to die first before you can eat it, so you'll probably wait a while, depending on how resourceful it is. Whether or not you thing long term or short term as a succubus, its still a while that you have to wait, and its still clipping your power for the wait.
The contract should grant power to the succubus to use like a bank to loan out to her deal makers. Sort of like when you go to university and you look for grants and partial scholarships. For having lots of students and good reports and various other things, the universities get money from the government (or private sources depending) and they can use that money to pay for people to go to their campus, make their college more well known and give them a better reputation, thus giving them more money. The contract would be somewhat similar to this. The university is the succubus, the government is the contract, and the student is the deal maker. That's kind of how I see it.
Also various shrines and temples, place of worship could also give the succubi a power boost. This would explain the construction of the hundreds of temples scattered throughout the Forests/Jungles. At one point, you get a large group of people to construct a large temple, with a library full of ancient knowledge and spells, and worship the succubus so that the leader and a few others get power, and grant her power so that they can use it to further their society. Or something along those lines.
These are my thoughts on the matter anyway.
edit: just note that if the contract is nothing but "you get my soul I get your power", its not short and sweet. It's actually bland, and exploitable. That's why this is a really important thread