1. About maximum reentry speed, unshielded.
Not an answer, just some additional elements...
From wikipedia:
"An approximate rule-of-thumb used by heat shield designers for
estimating peak shock layer temperature is to assume the air
temperature in kelvins to be equal to the entry speed in meters per
second."
(for vehicle speed see figure below).
Then it depends on the spacecraft material exposed to heat. The material must maintain its mechanical properties, and the temperature inside must be acceptable.
For current deorbit schedule, the reentry interface occurs at 102.3 km altitude, at 7,591 m/s. How much time will be needed for the compounds to melt at 7,823 °C (or the inside temperature unacceptable)?
figures will change when the reentry interface speed will be decreased, and so the landing trajectory.
2. About alternative atmosphere reentry methods
Alexander Bolonkin wrote an article (another version here) in which he proposes to use high-altitude parachutes to supplement or replace the heat shields.
Warning: The author looks like controversial.
"The widespread production of high temperature fibers and whiskers
allows us to design high temperature tolerant parachutes, which may be
used by space apparatus of all types for braking in a rarefied planet
atmosphere.
The parachute has open backside surface that rapidly emits
the heat radiation to outer space thereby quickly decreasing the
parachute temperature.
The proposed new method significantly decreases
the maximum temperature and heat flow to main space apparatus. That
decreases the heat protection mass and increases the useful load of
the spacecraft."
In the same article, he shows the effect on the STS orbiter (with different parachute sizes):
I don't know if this has been researched further, or even confirmed as valid.
