or maybe structure the organization as two parts, an independent trust that acts as a custodian with set aside assets to cover the running costs over the expected lifetime of the covered population , and a technology company that builds markets and operates the service on behalf of the trust (or trusts)?

kind of like how a regulated brokerage, pension fund or insurance company operates. The difficult part is credibly ensuring that the companies will follow the rules when there is no legal big stick hanging over them. Maybe you could have the company buy and issue performance bonds to the policy holders , so if the company disappears, the policy holder or their family gets a lump sum? And have the (independent) company issuing the bonds have the contractual right to display the current pricing of the performance bonds, so if the bond company starts to suspects mismanagement, the price goes up, and that has an immediate effect on the company’s standing (and is therefore likely to deter bad behavior)

Cryonics service providers do that. Here's an example from Alcor, the largest: https://www.alcor.org/library/the-alcor-patient-care-trusts/

"At Alcor, patient storage costs are paid from two separate but interrelated Trusts: the Alcor Patient Care Trust, and the Alcor Care Trust Supporting Organization. … This conservative funding arrangement is designed to cover the cost of patient storage solely from the income from the Trusts, thereby assuring that such funding will continue indefinitely into the future."

The oldest organizations are churches and universities. Seems like they should be involved managing something like this.

Banks and trusts management firms generally have a good track record. Lately banks have been much more speculative but historically existed because they had peoples trust. Trust management firms that manage trusts have to last because it’s part of the purpose of a trust. I’d imagine a digital trust could have potential, where you add some sort of digital artifact and it’s expected to be accessible.

Churches and universities are not something I would bet heavily on in the next 100 years. Some will survive, but society may not continue to favor them like we’ve seen recently.

Churches surely have ahem a hand in the afterlife planning of many people, and a good track record for being their at time of death, but they’ve recently taken a massive beating in terms of attendance in much of American.

Universities were pretty rare a long time ago, and society has seen lots of new ones recently. I don’t know if I’d bet that any but the biggest names (endowments) eg ivy leagues, Oxford etc. can be counted on to last another hundred+ years.