Running propellers in opposite directions to help swing the ship is only really effective while maneuvering with the ship barely moving, and takes a looong time. At full service speed the water would just stall/cavitate around he reversed prop.
The strain on the framing, blades, and shafting would make it very very risky.
I believe that they rang down 'Stop' prior to collision to avoid the fear utmost in their minds, having a turning prop striking the berg.
At last! A bit of common sense.
Your "belief" is spot on.
No experienced bridge officer would touch the engines if the intention was to steer the ship out of danger. However, the second the starboard bow hit
any underwater obstruction - let alone ice - the first thought would be for the propellers.
During a hard LH turn, on a twin-screw ship, you would stop both props. Because if you simply stopped the starboard one, the thrust of the port one would negate any LH turning motion, and, as you say, the rudder would be useless due to turbulence and cavitation.
Unfortunately, when Murdoch stopped both props, the turbulence caused by them and the dragging center prop. would have rendered the rudder useless in a very short period of time.
By the way, having actually maneuvered ships driven by triple expansion engines, I can confirm that an emergency request for full astern was normally a two-part action-- STOP...then Full astern and always with a double ring. (telegraphs were chain-driven in the "olden days".
If I remember correctly, the reason for this was that four sets of rings in a noisy engine room would be heard as prolonged alarm-sounding bells which would be sure to be heard and immediately recognised as an emergency. Then, of course, there was also the changeover procedure from ahead to astern which took time and effort.