小手先で済ませるよりは結局早く終わるだろうと: thinking it will eventually be finished earlier than to settle it down superficially
- "it's better to finish it early" would be 早く終わらせるべき
分解しつつ片っ端から手をつけていったら: as I dissembled it and
take took every single piece in sight
- したら = when I do, していったら = as I do
完全にバラしてまた組み直すような真似をしていた: I found myself doing something like thoroughly dissembling and reassembling it again.
- まね basically means mimicking but here it's used to express how pointless the work was, though he was actually doing it.
Edit: ～ていく means
- do something somewhere and left there e.g. 食べていこう: let's eat it before we go
- the action evolves to the direction away from the point-of-view e.g. 押していけ: push forward
- something gradually changes or result of a recursive action accumulates e.g. 無数の星が消えていく: countless stars vanish
es one after another
In this case, it's used in the third sense and していったら instead of simple したら means he recognized himself in the course of the work, not so much as he worked, then recognized.