Trick that I'm trying to use on getting high pops....
Many posts here talk about using using transports to move pop off of a planet and keep morale high.
Take those transports as you build to invade and park them in orbit around a high pop capable planet.
As you build up your invasion forces, it increases the population of select planets since the increase is a percentage of the total current population.
It works great if you can have several high pop worlds on your borders...use them as rally points.
By the time you send your troops to invade, those worlds will get the benefits of those troops in population each turn.
On morale, pop morale negatives stop at 80%.
So on high PQ planets, all you need is to negate the 80% pop morale penalty and control the morale penalty due to tax rate. Put the rest into stock markets and farms....(havent figured out the best benefits from amount of stock markets versus population, there should be but I'm too lazy

)
It takes a while to build up pop, so its better to start early and control morale via tax slider and rsearch.