Very slow turn-on time BJT (BUV27)
The t(on) time of the BUV27 is very high (400-800µs) compared to the
  storage/turn-off times (0.5µs/0.12 µs). Why is this so?


It's a typo - they meant to say micro seconds as per this data sheet from an alternative supplier: -



It's always worth digging around to get to the bottm of things if something looks suspicious. I note that both ST and ON semi have made the same error on the data sheets.


  How would I go about finding a replacement?


You start by analysing the circuit and then trying simulations with different transistors - you can't expect to find a replacement by only comparing data sheets.