One avenue I would explore
1 is the following:
The Venerable Old Leader (VOL) who originally summoned the spirit discovered a ritual that transfers to-what a bound spirit is bound to, specifically the ritual binds a spirit not to a person, or even an object, but to a title/position of power. So at some time the VOL, realizing he/she'll kick the mortal coil like everyone else at some point, gets his cult together (or at least the magically active members) and performs the ritual binding the spirit to the title of "Venerable Old Leader." Now when the original VOL leader dies and the title of VOL is passed on, so does the spirit's services and "bindings."
One could set up that if a new VOL isn't selected in a certain amount of time (original ritual hits times days/weeks/months, or just a static year-and-a-day, etc.) then the spirit is freed.
The ceremony of electing/recognizing/establishing the new VOL is also a ritual that re-attunes the spirit to the cult and it's (new) leader, so as to fortify the spirit against random guys on the street saying "I'm the new VOL" or rival cults using the same names, etc. in addition to replenishing bound services if needed. These rituals, in addition to binding the spirit to a title, create the pattern of the specific cult from which the title emerges. Where there may be many cults who call their leader "pope," performing the ritual binds the spirit to the title of "pope" specific to the believers of a unique group.
A GM could have fun with this and include spirits bound to the draconic "Lore Keeper" or the Catholic Pope or the President of UCAS and so on.
As for devil or angel.
So the "heir" is going to need to be a pretty competent conjurer him/herself, and effectively TAKE the spirit away, though the taking will be consensual.
...I want to present the binding as very forced ... and demeaning...So I'm coming to like the idea of the spirit being, in the binder's mind's eye, a bound devil. Thoughts?
By "consensual" do you mean between the original summoner and the heir and
not between the heir and the spirit?
If the group is fundamental Christian (as currently understood) then an angel would be seen as a gift from God, to be honored, feared, and to rejoice over. But brokering with a devil is right out. The Gospels are full of Jesus driving out demons/devils and resisting their temptation and any members of a fundamental Christian group would see that as their only actions towards entities identified as such by them. The "fundamental" part means a strict and literal reading of the sacred texts and as such devils and demons are to be cast out, banished, and destroyed...nothing else.
2This is not to say that some members may do so in secret, only that it would throw out my bind-to-title ritual which would require the acceptance of the group and that using the spirit formula route as suggested by CitizenJoe and Mirikon would be better suited to the task. But you still run into the issue of the individual or people in the group using the devil would be doing so secretly. I would say, if you want to use a "classical" fundamental Christian group then make the spirit an angel, with all the love, honor, and light heaped upon it by the group, and use what the group does to outsiders, unbelievers, etc. as an indication of the group's not-so-friendly attitudes (i.e. they seem to ignore the whole "love thy neighbor" and "turn the other cheek" ideals).
Of course there's lots of room to play here, so you could make the group far enough outside the mainstream Christian thought; allowing within their group the binding and use of devils...but doing so would alienate the group to the vast majority of Christian groups.
1 "Explore" meaning see if there's any RAW to support it and if not make up a house rule for it.
2 In this and the following paragraphs I'm only speaking generally and not attempting to make any judgements on any current real-world religious organizations, groups, or individuals.