It's really hard to say without knowing the conditions of the people you're targeting for aid but ondols, kangs, and rocket mass heaters are a really good solution for creating thermal mass to use as a thermal battery but they are also quite permanent so its much less suitable as a solution for people who are homeless/housing insecure that are more transient (i.e. compared to living in slums or shanties which are permanent or semi-permanent.)

If you are intending on using this sort of heating method for people who are unfamiliar with safe operating, a rocket mass heater is going to be the safest based on the fact that you are able to build this above-ground as opposed to it being underfloor. (Kangs are usually raised platforms but due to construction there are specific considerations for fire safety so I'll put them aside for simplicity's sake.) The only caveats are that a rocket stove needs to have a clear outlet free from combustible materials nearby. For people who are unfamiliar with operating a rocket mass heater who may have impaired judgement due to things like severe mental illness or substance use disorder, I would strongly advise having a straight exhaust as one which curves creates corners that creosote can accumulate upon. Suboptimal operation of a rocket stove will also create more creosote. Straight exhausts are far easier to clear and to visually identify when there is buildup. Realistic worst case scenario you're probably going to have is the exhaust shooting out a few feet of flame as the built up creosote ignites so you want clearance especially with suboptimal operating conditions and a lack of routine maintenance.

For transient populations, it's going to be about what is most portable - so stuff that is lightweight and ideally that packs down or can be easily disassembled and reassembled.

For permanent and semi-permanent populations things like cost and safety of longer-term operation become much more of a consideration.

I'm not sure what the weather is like where you are but if you're only in the early stages of planning I think you might have left your run to late for making a rocket mass heater that uses cob as the thermal mass. I'm assuming that you don't have a location picked out yet and that this is an org that meets once or twice on the weekend before everyone goes back to their day jobs but at a very optimistic timeframe it would look like everything being settled this weekend, including site and sourcing inputs, then the next two weekends constructing with it being ready to go by mid-January. That's assuming that everyone is happy with working through Christmas on this too.

I'm presuming a level of familiarity with cob construction and rocket mass heater construction. If it's a first time job it could easily take an extra couple of weekends. So I'm not sure exactly where that would leave you with regard to the viability of the project and your time frames.

I've never fired cob directly after construction. I would assume that it wouldn't be catastrophic but you could expect to see larger, structural cracks in the cob mass as it dries rapidly due to heat and the inner parts contract much faster than the outer parts. The temp of a rocket mass heater can reach vitrification levels so I'm unsure of the implications of this for the structure of an uncured cob mass - generally speaking cob is easily repaired with patching it however if uncured clay begins to vitrify when it's right beside the burn chamber it might not be so easy to repair and I'm not really sure where to look to find out if anyone has attempted this or what the short and long term results from it would be.

Cob also takes a surprising amount of effort and inputs. I'd strongly recommend using a small cement mixer to make your cob because otherwise the labour input will be very high - this is fine if you have a lot of people and the weather is decent, especially if you are building a lot of walls so you are limited by how high each layer can be constructed before you have to leave it to cure in order to prevent sagging but it's less ideal if you are trying to turn out a rocket mass heater in one day.

Do you know the soil composition of the site that you're considering? This is going to be a major factor with costs and logistics. It's not uncommon that you will need to source one of the two main parts (either sand or clay) to get the ratio right. If you are planning on using what you have on hand then it's possible that you're going to want to use a backhoe or mini excavator to save a large amount of time that digging below the topsoil would take to do manually but it depends on the size of the project and what you have access to including labour power.

Sorry to be a downer about this. I really like cob construction - I'm a big fan of it, although the skin on my feet is too delicate (probably EDS skin) and whenever I've made cob traditionally I always find that any small stones or pebbles end up tearing up my feet so this probably my one and only true complaint that I have about cob lol. It's really not like me to try and ruin someone's enthusiasm for it.

(Ooh look at me! I'm not just a grass-toucher, I'll even brag about having touched dirt!!)

Edit: I completely overlooked my assumption that this was intended to be constructed indoors or, at the very least, in a well-sheltered location (because I figured ondol = inside a home or sheltered location).

If this construction is intended to be outdoors or in a place which is only partially sheltered then it's going to become a lot more complicated and, honestly, unless you are pretty familiar with cob construction I'd just advise against it.

Cob can be used in outdoor construction and it can work well however it comes with significant considerations about the local conditions. Outdoor cob construction in areas that have high groundwater or on low elevation like, idk, Florida sounds like a disaster for outdoor cob construction except if you built on a relatively high elevation for the local area on a site that had sufficient drainange (this is well outside my wheelhouse). Heavy rainfall is going to kill it except under certain circumstances that would take a lot of effort to describe but if you are unsure about this then take it as your sign that it's a bad idea because its really not for beginners. As for areas that get any significant amount of snow this, too, is outside my wheelhouse. My hunch is that unless the rocket stove is being operated on a daily/near daily basis that snowpack piling up on the stove could cause serious problems with getting the exhaust to draft and getting it up to optimal operating temperature - not impossible but unlikely that it would be an easy task and unlikely to be something for beginners. As for snow melt and the damage it could do to a rocket mass heater, again that's way outside my knowledge but it's possible that it could destroy the cob mass, requiring either a major repair job or even a complete teardown and rebuild. Hard to say for sure and it's never something that I've had to consider so this is just speculation.