"And without needing the complex technology involved?

I have the feeling the water weight will be a major issue, but I figure
since the astronauts need to drink anyway, plus the engines and
other systems may need water for various reasons...."

I think that about 1 foot of water would significantly reduce the radiation.
Shorten the time of the trip, equally reduces the radiation.

I would "trade" lots of rocket fuel for shorten trip time- and perhaps addition have say 6" of water for shielding around all living quarters- plus have solar flare shelter- maybe as much as 2' of water in small space for crew.
In addition if you go there fast, you will need a fair amount rocket for braking once you reach Mars- that should also be configured so it acts as even more shielding.

So burn lots of rocket fuel and get to Mars in 4 months [more or less]. Use more rocket to brake. Refuel rocket in Mars orbit. Repeat on way back to Earth [4 months] and braking at Earth.
Getting lots of rocket fuel to Earth orbit and Mars orbit would be fairly cheap.
Figure about $10,000 per lb at Mars orbit and about 6000 per lb at Earth orbit. So per 100 tons: $2 billion and $1.2 billion.

So you have a ferry that goes back and forth from Mars using about $3 billion in fuel per round trip. You replace the engines when needed. And after say 10 trips you scrap it, or use it for slow freight or whatever.

Ideally, I would want lunar water used, but if you simply ship rocket fuel in bulk from Earth using commercial launch vehicles you could get a fairly low cost per ton

Cargo and fuel [anything without crew] can be sent the long transfer of 8-9 months.