There is few problems, which are not medially spoken, or unsolved - out of discussion at all.
- Time necessary to get those people up
- Original shafts
- Current communication channel
- Current security of miners
Those four months, from original solution, maybe includes respect to further usage of pits. This is first thing: if its so, then it would be much better to absolutely renew rescue plan, even if further mining in area would be harder or impossible!
Also, those plans are computed using present mining equipment, which is designed to mine, not to rescue, to sell, not to offer needed parameters: time of four or even two months smells of unfortunate optimism, rising from being in contact - so unsure.
The basical forcing of plans should be done, rising from support of worlds community - at least here, where there is not eight millions of endangered, and where technology and science is a least and last base of solution. There should be investment to development of new technique, maybe with high regard for actual geological structure and options of area: high resolution study of terrain should be done, given to worlds science community, to develop maximally secure and fast solution. New machine, or set of machines, respecting different geological layers and their options, limitations and dangers. Also, there should be much more fear, here on surface, and so different things given to the people down: security constructions, oxygen, water and NASA food (good idea), of course. Being more skeptical means making ourself sure, they have reserves and different tools for themself, for any case! Maybe there is more of danger than just rock blocking... fire - water - psychosis (after serie of accidents, following isolation).
Communication shaft should be considered as highly instable, the same as space where people are currently still alive.
Thinking that they will surely die, is what is to be felt. Making long plans and speculating on depressions is crazyness. Of course there should be even improved communication between families and workers down, but it should stay just far behind other things, being just middle for them and their families!
There should be maximal number of parallel plans and constructions! Some of them as attempt for maximal speed some of them for a maximal security of construction for TDW*. If the first class succeeds, they will be rescued in days (explosives? acids? ...), if all other attempts fail, there will be one or two running, where work is as slow as needed, to conserve every taken step of rescue construction against any kind of failure (even if it would required making five coordinated shafts, and two of them built from tons of steel. There should be, under bit more than required security pressure, also parallely running attempt to reopen original shafts: as zig zag ones, as orthogonal ones.
Communication shaft should be considered as highly instable. It should be used maximally, to put tools, reserves down. All its failures should be considered and prevented. It should be stabilized also, not really used for another work, as for example rescue shaft. Some using of it, is just step to field of dense, random accidents. There should be just half of unsure time of this shaft for material communication, and half of it for making it more stable, more persistent, more effective! Definitely its treasure! Or maybe make few more, also...
Miners should get some stable, secure, and full time communication tools. They should get as much construction components as possible, to start to work, in order to make sure, that not even small grit can fall on their head, and not even piece of "wall" will rain down, until they wish so. They should get also distinct chemicals and medicines, in order to prevent any kind of troubles, as they were PLANNED to keep them there for YEAR. They should get energy, and also relaxation things, as they were on a red dwarf with king of potatoe planet. Food reserves, medical oxygen, medical tools, army tools, maybe even special explosives... Maybe even some small oxygen and water generation and recyclation unit, if there is such! Speaking of two or four months in the future tense is just clean proof, that they will die in week, and clean symptom of curiosity-centrism of surface world, which is just consuming healthy skepticism, working reason, just because people on both sides are dangerously enough with having 700 m long hole of not even 15 cm in diameter. I don't believe someone would undergo such "circus horror attraction" even for one day.
1) TDW Top-Down workers, DTW Down-Top workers, regarding the target, that both sides are working for rescue. Only acceptable reason for people down to not work for themself is, when there is more than 20% risk for them to loose some helping condition OR LIFE, when working. If anything fails, and they have no equipment more, than pocket knife and industrial machines, they will commit suicide, or die from madness. They should work a) to stabilize the space, b) to make sustainable environment, c) to make reserves, d) to get out ... which will keep them cooperating, having faith, keeping them out of psychosis, nihilism etc.