~をかわきりに(~を皮切りに)      => One after another; starting with ~ N1
切る => Give up, stop... N3
Happens next
切る/切れる/切れない => to do something completely to the end/unable to do; too much to finish/complete N3
直ちに => at once; immediately; directly; in person; automatically ~ N2
て仕方がない/てしょうがない => can't help but; very; extremely ~ N2
[切「き」]れない => Can't finish/complete A N3
Potential, Possibility
…たりしたら/しては => ... Such as N3
Demonstrate by example
より(も)むしろ => rather; instead; better ~ N3
かりに...ても / としても => even if N2
Condition (hypothetical condition)
... ほしいばかりに => just because I want to… N2
Cause, reason
…たりして => maybe, It could be, it is possible that… N3
Demonstrate by example
たりなんかして => besides, there are things similar to that N2
Demonstrate by example