Here's one trick i've used at times to maintain relatively "high" morale on my Homeworlds.
Loading up an armada of Advanced-Transports to the rim which, indirectly, puts some population in idle mode. Those can rapidly level down a 17+ to a more manageable 12 or even less!

Sometimes i also transfer lots of population in
freshly founded or conquered planets... the above armada, then, becomes a welcomed asset since the parked
growth only takes a few turns of travel (Hyperwarp can do marvels, Constructors & Freighters DO get the advantages of maxed engines quite often too, btw.) to realize a swift pop-cap maximum on each planets as desired.
As stated above, the Political Capital is a
must when the 20bils wall has been reached. And yet again, i believe there's another indirect way; The Good & Evil techno branch has some Morale+ features which should be quickly researched if you want to prevent losing chunks of 5 to 10% worth of taxes just to keep everyone on HW happy enough to tag a 60%+ value instead of a reddy 40%-. Although, the overall numbers on all other planets can compensate for this effect... in the long run you would need an almost permanent solution which, in turn, may prove unnecessary since, at that stage, i'm 90% sure that a victory condition is right nearby within a matter weeks -- unless, you plan on conquering everything up to the last men standing!

Hope the above made sense.
- Zyxpsilon.