Get letters from both GP and oncologist.
Definitely include health status, treatment details and associated fatigue, lack of family support, need to increase hours of care. Include lowered immunity, and fortnightly spend on childcare. As for increased costs, absolutely include naturopath, phramacy costs and travel and parking expenses. Increased food costs (although I 100% support you doing it and believe in it wholeheartedly) is perhaps stretching it a bit far.
I wouldn't stress too much about justifying your LWOP situation.

But, look, I've seen quite a few parents get it with less ammo than what you've got, so go for it. Good luck, thinking of you!