We solved that problem in the 1960s with Apollo
and the Soyuz was originally designed as the Soviet lunar spacecraft, so the modifications aren't exactly something that have to be invented, just reapplied to the Soyuz.
For the radiation protection, there are some options, including accepting a higher radiation exposure as part of the overall mission risk. Other than that, increased shielding techniques are understood. It wouldn't necessarily require a bunch of heavy shielding (e.g. lead) but perhaps just more shielding than is presently installed for orbital missions.