There's a bunch of techs you can research to reduce the attrition rates - mountain/jungle warfare tech, first aid, combat medecine... are those not helping?
I got the Jungle one ages ago, I have started making sure that first aid, combat medicine and agriculture are always being researched. However, it is much harder to tech rush in 1.3.
Ho much manpower do you have? How much is the daily gain? How many para divisions do you have? What difficulty are you playing on?
Manpower is hovering between 0 and 100. Not sure about the daily gain, but before war with America the monthly increase is about 77. So I make that to be ~ 2.5 manpower per day.
I ended up halving the size of all the divisions defending the Japanese mainland. I originally had a division of 4 infantry brigades on each port. Now there are only 2. I used the manpower from that to build more paratroopers taking my total to around 78 divisions of 5 brigades each (390 Brigades). (Need to double check that I am not 100% certain). I think I only have 2 more divisions in production just now.
Difficulty is normal.
I played through quite a bit last night and got screens but did not have time to write it up. Basically Haiti -> Bermuda -> Florida... Was very good fun, quite epic. LOTS of USA troops but most of them under strength. Some nice encirclements and the first time I have had to retreat paratroopers from a battle that was going sour.
I am very glad there was not much time between DoW and getting troops attacking USA mainland. If all the divisions I faced were 100% strength instead of 25%... I will try to post details and screens tonight.