It would interesting to know just which auto-pilot was installed in that aircraft. I few Lear 24s (oval cabin windows) back in the mid 70s that had the Lear auto-pilot installed, which at that time was the only auto-pilot that was available for the Lear 24, not sure about the 25 series.
My reason for inquiring is, back then the only time we used the Lear auto-pilot was at cruise. All climbs and descents/approaches were hand flown due to the mistrust of the Lear brand auto-pilot.
As for the speed used in climb, above 10,000 feet we would climb on the barber pole. About every Lear 24/25 pilot I met back then did the same. We did not have the illegal 'Mach' cut out switch in our 24s.
As far as the 'coffin' corner is concerned, at FL280, I believe that would not be an issue.
Hopefully the CVR will be able to shed some light on this accident, if it was working.