I've been doing a little light reading in "the Pre-Astronauts"

Yevgeny Andreyev an expert sky diver prior to his record Stratospheric Jump claimed he controlled his spinning with hands and body positioning. Kittinger seems to have no problem using the BMSP system of chutes to control spin after his first dive. Some nice video out there if you search on Kittinger...even one were they altered reality and have Joe surfing at the end of the third jump...8-)

I think with hundreds of suborbital flights planned maybe an investment into resurrection of Beaupre multi-stage parachute (BMSP) system might make some sense.

Yet the long-term legacy of Project Excelsior is not without its dis-
appointments. For one, the Air Force never adopted the Beaupre mul-
tistage chute for high-altitude pilots and never developed an adequate
high-altitude pilot ejection system. Instead, the prevailing dictum was
that pilots should remain with their aircraft until they were back down
into the lower atmosphere before ejecting. Parachutes were eventually
added to both high-altitude aircraft and spacecraft, but no real provision
was made for escape from a burning jet at higher stratospheric altitudes,
Air Force statistics on survival rates of pilots who eject above 40,000
feet with a standard parachute are grim indeed.

Nor was NASA very interested in the Excelsior-style survival system.
Kittinger and Stapp were convinced that it was mostly politics. Why
should a huge organization like NASA, already operating in what Tom
Wolfe would call the "billion-volt, limitless-budget future" even take
notice of a two-bit bootleg balloon program run by renegade doctors and
test pilots? All three Excelsior jumps had been accomplished for a total
cash outlay of about $30,000, a trivial amount that was within the mar-
gin of error on NASA ledgers.

Page 222