Not sure I agree pace,
1) engine that takes out hydraulic pump so you are unable to retract flaps and gear, it's not going to want to climb well at all.
2) engine failure at vr or very shortly after, identifying the issue, reaction time, lowering nose to get v2 with gear and flaps out . Dealing with the failure, power, prop, fuel assuming no AF, controlling aircraft, gear and flaps maybe a fire to add into the mix. At best you maybe 15-20 seconds into the flight, sinking as you raise the flaps, even if you did it all by the book and start to get a positive rate of climb I'd bet 30 seconds would be gone.. There's a reason engine failure is assumed above 200ft!
You only have to do a go around at minimum to know a TP at vref is a handful, this is with an already feathered prop and 20knts more than you you have at vr, add in the drag of gear and flaps and you're lucky to maintain height..