44. & 45.
君はなんとなく手をつくした気になって自分を納得させたいだけど
However, you somehow feel as to try all possibilities and want to convince yourself
君 は なんとなく 手をつくした 気になって 自分 を 納得 させたい だけど
you [topic] for.some.reason to.try.all.possible.means+past to.worry.about+TE oneself [object] agreement to.do+causative+tai however
A quite difficult one…
First I thought it was:
手をつく is a set phrase; to put the hands on the ground, like when doing 座礼 (ざれい) (sitting salute); it denotes great respect, or very humble demand.
It is treated as a nount, with する to make it a verb
But actually it is
手を尽くす : to make everything possible.
納得(なっとく)する : at first I thought it was to consent, so that Saitou wanted consent from Pr. Shiratori… but it also has the meaning of agreement, understanding. So 自分を納得させる is more like convincing oneself.
自分を納得させたい : you want to convince yourself. It is however a very strong wording (usually ~たい is only used for oneself, not when referring to others)
or maybe I’m wrong 
そんな 自己 満足 に 投じる 大金 は ない！
about transcription...
Again I have been in the strange situation, where I could guess reading and type じこまんぞく without knowing the meaning…
There aren't large amounts of money to throw in such self complacent manner
そんな 自己 満足 に 投じる 大金 は ない！
that.manner self complacency [purpose] to.invest/throw big.money [topic] there.is.not
自己 (じこ) : self-
満足 (まんぞく) : complacency. 自己満足に is an adverb
投じる (とうじる) : 1. to throw, 2. to invest money
大金 (おおがね) : big amount of money