To the OP: the short answer is yes.
I have just come back from three weeks in England and Ireland with the K-1 and the following lenses:
DA10-17, DFA15-30, FA31, DA*55, FA77, DFA100WR and HD55-300
The 55-300 worked brilliantly in crop mode. The few times I used it in FF mode it was clear that it covers more than APS-C at all focal lengths, but not the full frame. The DA10-17 actually covers the full frame from about 15mm, but its edge performance suffers enough for me to still consider it a crop lens.
Some examples with the HD55-300 in crop mode:
And this was moving FAST towards me. This car won Le Mans a week or two before this was taken - we were staying with the boss of the Ford racing team
And with the DA10-17:
Your 40 and 50 (or do you mean *55?) are also FF compatible.