QUESTION:
Did you consider the use of a parachute similar to the types connected to
small personal airplanes that can be deployed at high speeds and have a
mechanism to continually allow the parachute to expand as it slows?

ANSWER from David Dubov:
You are stumping the "expert". I am really not at all close to being a
parachute expert (despite my pontificating). I am sure you are quite correct
that new more complex parachute designs could very well be developed along
the lines you propose.

I do know that there are big challenges associated with the qualification
(design verification) of parachutes destined to be used on Mars, especially
if they are required to be opened at supersonic speeds as ours is (Mach
1.7). It is quite difficult to reproduce the opening conditions on Earth.
Wind tunnels have their drawbacks (size & wall effects) and high-altitude
high-mach number tests are very expensive (out of our league for Mars
Pathfinder). That is why we did not consider more complex designs. In fact,
a going-in position at the beginning was that we would save money by
borrowing the design and test results from the billion-dollar Viking mission
from 20 years ago.

For chutes that open up at low speeds (say after a drag chute has slowed the
lander down), then maybe the problem could be solved more cost effectively.
It is a fun and potentially quite useful solution that should be explored.
(Imaging a chute you could "steer" right to your favorite landing site!)
There are many more design solutions yet to be discovered!!