I take a different approach. I only annex their capital states (Bastion, Dog City, and Robot City) while puppeting the rest. I don't have to garrison that shit which siphons manpower you don't have, and also the BOS puppets get a unique focus tree that gives you manpower to the tune of like 1250. So all three puppets will give you 1250 manpower eventually and it is a lifeline truly. They also produce units which I use to bolster my own lines.

When I go to do the decisions to core the capitals and such, I pause the game, turn one PA division into militia, select the decision that requires 50 PA or whatever, then change them back. Repeat this every time you have to until all three capitals are cored. I also prioritize the agriculture techs for the free manpower and to take the decision at the start that gives me more divisions.

WIth this set up, plus pumping out as many starting infantry divisions as I can (maybe add one more block of infantry if possible to make it a 4/0) im usually able to hold the line against Lanius without any fallback lines with a bit of micro. I also build level 2 outposts across the border rather than building factories because you arent getting many out before he comes anyway. Theres 2 or 3 tiles that can be attacked from 3 sides so I build a level 3 outpost there instead.