Supposing that the 4thSW's 100 million deaths are primarily infantry, and supposing the defenders suffer twice the casualties of the invaders, then defending planets lose about 5 million infantry per month while the invaders lose about 2.5 million per month. If you figure 2.5 million guys at 5 tons each, and a Mammoth (or half a Behemoth) at 40 kilotons* of cargo, that uses only about 320 DropShips (per month of travel), out of thousands of such ships sphere-wide.
As for the defenders, I count significant fighting on roughly 140 worlds, including:
Confederation- Tall Trees, Zurich, Aldebaran, Liao, Bharat, Tigress, Tikonov, New Hessen, Styk, Wei, Truth and Sarna. (The Duchy of Andurien attacked some worlds too, but it's not clear which ones.)These 25 worlds have a combined population of somewhere near 65 billion people; at the Tikonov ratio, that makes 492.4 militia regiments. Supposing the other 115 worlds have two battalions apiece, that would make 569 militia regiments in all.
Combine- Buckminster, Kirkbach, Radstadt, Altair, and Vega.
Suns- Marduk and Kathil (whose populations I don't know), Algot, New Aragon and Halloran.
Commonwealth- Tamar and Poulsbo (whose populations I don't know).
Free Worlds- Procyon.
From HM:FWL*, an infantry battalion consists of 400-500 people. 7 troopers per squad and 36 squads per battalion would be 252 troops, and a tooth:tail ratio of 1:1 would bring it up to 500 troops. (The 400-person battalion may be Jump infantry, which use smaller platoons.) At 3 battalions per regiment, my estimated 569 militia regiments would amount to 860k troops. With losses of 5 million troopers per month, these militia units would seem to have an expected life span of five days. Or to put it another way, a population of 44 million has a standing force of about 1000 troopers, and can call up another thousand every five days. This is something (I can't find consistent data on it) like 6x-8x slower than nations mobilized for WW2.
Of course, the tooth:tail should be more like 2:3 or even 1:3 instead of 1:1, many of those worlds won't have a full 44 million people, I'm arbitrarily excluding the House's regular army and navy, and I'm ignoring how late the fighting started or how early it ended on any given world. So the worlds attacked in the 4thSW may well be mobilizing at WW2 rates.
*Curiously, that makes the Mammoth's 40 kton cargohold just the right size to carry a FWL infantry division.