Sorry - didn't mean to make work for you - but unfortunately once design questions are raised then that sort of needs a modicum of design details to be collated.
Regarding the FET, it is often about listing the available options you can obtain that generally meet the protection limits (eg. Vds in this case), and then hone in on package type that suits the application, and then look for trade-offs between Qg and Coss and Rds-on - and even then if you're keen the outcome would be to purchase the likely best 2-3 models, and try each of them under standard conditions. It's not easy to compare final efficiency, as the frequency and duty cycle and drive capability and parasitic loop inductance and capacitances may all have some impact.
Is 150mA the peak current at turn-off ?
Do you get any transient overshoot in Vds? You may need a good oscilloscope and probe and probing technique (ie. not just standard ground wire and alligator clip).
Regarding the FET, it is often about listing the available options you can obtain that generally meet the protection limits (eg. Vds in this case), and then hone in on package type that suits the application, and then look for trade-offs between Qg and Coss and Rds-on - and even then if you're keen the outcome would be to purchase the likely best 2-3 models, and try each of them under standard conditions. It's not easy to compare final efficiency, as the frequency and duty cycle and drive capability and parasitic loop inductance and capacitances may all have some impact.
Is 150mA the peak current at turn-off ?
Do you get any transient overshoot in Vds? You may need a good oscilloscope and probe and probing technique (ie. not just standard ground wire and alligator clip).