You have most of it right. Some things you have wrong,

1. Desiel injection timing is differant than on an Otto engine. The
fuel is injected during the intake cycle on the Otto engine and the
fuel is injected during the ignition cycle on the Desiel. On the
Desiel the fuel injection cycle starts just before TDC and ends well
after TDC. The fuel ignites as soon as it hits the hot air.

2. The parts count is not less on a two stroke Desiel, It is higher
because of the need for a supercharger and a way to port the exhaust.

I don't think you would want a four stroke Desiel in an aircraft
because of the increased weight and low power. Desiel engines don't
really produce more torque as a gas engine, its just that the fuel
burns slower and thus the engine cannot rev as fast, but it can produce
the same or slightly more torque at lower speeds, and at much lower
fuel flow rates. Because of this they should be ideal for an aircraft
engine that doesn't need to turn at a higher speed.

You do lose one advantage of the Desiel engine on an aircraft. Because
of the lack of a throttle and the fact that they can burn extreamly
lean at idle, Desiel engines are extremely efficient in stop and go
traffic. But we don't idle aircraft engines that much.