Isn't the connection between Zarya and Zvezda different from the conventional Progress docking port? Would it be possible to re-dock Pirs or Poisk from the aft port of Zarya?
Other than that, I think propulsion is the primary problem. Obviously some sort of hypergolic Russian upper stage would be the first choice, but it would also have to be modified to connect with the spacecraft and for everything to operate as a single unit.
Is radiation really that much of a problem? What is the difference between the exposure to GCR in LEO and exposure beyond the Van Allen belt?
Also, what of the option of aligning the spacecraft so that the maximum amount of mass is between the crew and the Sun? Maybe this could at least be of help during a solar flare (I believe doing this in the event of a flare was suggested on Apollo).
Obviously the mission would be absurdly dangerous, but a mission with even an 80% chance of death is better than a mission with 100% chance of death...
The ideal candidates might be older cosmonauts who are willing to take on such a dangerous mission. Being older will mean they will also likely be more experienced, which is a good factor in a mission such as this.
Assuming a Mars escape velocity of 4000 m/s and an exhaust velocity of 3196 m/s, a mass ratio of 3.6 would be required to break out of Mars orbit. Assuming a stage dry mass of 5000 kg and a propellant mass of 19 000 kg, roughly seven or eight stages would have to be clustered for a 38 ton spacecraft (7200 kilogram Soyuz, 19 000 kilogram core module, 11.8 tons of... other stuff).
It should be noted that Zvezda particularly, has its own propellant supply to assist in attitude control and reboosting of the ISS. This presumably adds a lot of mass, a good deal of which could potentially be removed for a Mars mission.
Nauka is scheduled to be launched; perhaps it would make a better habitat/core module.
A Mars flyby could be far less demanding and still allow a return. However, the scientific return of such a mission vs. cost would likely be far lower.
Aerobraking has been used by certain Mars probes; I am not sure of its efficacy in this case. Presumably lightweight 'drag panels' could be used to increase aerobraking potential, along with the solar panels on the vehicle. Attaining a circular orbit would likely require many months of aerobraking procedures, which could take up most of the Mars stay time.
Perhaps partial rocket braking would be a good idea, this would require propellant, but perhaps not as much as a full MOI burn.
The main spacecraft and the return stage could be launched seperately to reduce the size of the EDS cluster.
Overall, everything would be very marginal, and very risky with such a low development time and no test flights. The lack of high-performance Russian upper-stages is very limiting. The US posesses a better stage in the form of the Centaur, but does not have the manned capability that Russia does. In addition, boiloff mitigation systems, connectors and control systems would have to be added to the Centaur stage.
Connectors and control systems would also have to be added to a Briz-M derived stage, however the propellants inside are storable and thus perfect in a logistical sense for MOI and TEI, if not perfect performance-wise.
If I'm not mistaken, modifications would have to be made to a Soyuz return capsule.
Such a mission could only be flown within a significant lead-time, which might be 1-2 years. All the required launches would likely usurp all or most Proton rockets available for commercial satellite launches. Cost would be another issue: to ensure proper development and operation, a large amount of money would need to go towards this program. The USA could be of assistance here, as a tiny amount of the huge US defence budget could be shunted towards funding mission development in Russia, for the exchange of flying an American cosmonaut to Mars.
Overall the whole thing really makes you wish about having an Energia-lifted high-energy upper stage as a nice quick solution, or a better habitat architecture, or a nuclear propulsion stage. Without a dedicated architecture, or at least a flexible architecture able to accomodate such flights, such a mission is marginal in its potential for success, and horribly risky.
If we just had that architecture, the enabling architecture for BEO operations, it would make things far, far easier. We don't have that architecture presently, and we've never had it in the entire history of spaceflight.
