Re: This sounds a bit odd.
The drogue parachute (the only part of the ejector seat relevant to this discussion) fires after the seat starts descending.
No, that's not true.
The seat is lifted from the airframe either by cannon (old-style seat) or rocket (new style, somewhat easier on the pilot). As it lifts, there are two straps (extendible rod-type things) between the seat and the airframe; as they reach full extension, one triggers the barostat to start the chute deployment sequence, and the other fires a rocket which deploys the drogue chute from the headrest.
A cable from the drogue ends in a shackle which is held in a pincer arrangement at the top of the seat. This allows the seat to be suspended from the drogue alone. Once the barostat finishes, the seat chassis is released from the harness (and falls away), and the pincer is released, allowing the drogue to pull out the main parachute.
Any earlier and the seat would just tangle with the drogue before it opened
No. The drogue is fired from the seat (and after the seat has already started moving), and is rocket-powered.
The extra lift given by the rocket assist is to get the seat occupant up to parachute height
Not so. The rocket ejection system is used to spread the total impulse over a longer time period, leading to lower forces acting on the pilot. This makes life easier for the pilot. But the old-style cannon ejectors could get the pilot plenty high enough - just with a risk of damage.