How do you think a burst tyre will result in a severe of both A and B reservoir lines on a 737? Would it be physically possible?
I guess not,no way for some piece from the burst tyre to enter the main wheel and severe the lines.
Even if this would be possible you'll have the stby sys for take-off.After that,even with stby disabled,an engine out would be survivable at higher speeds. For landing,I'll do as you said,come to a good position,then reduce the working engine,and glide for landing. (done in the sim,210 kts,flaps up,both eng off,did ok).
To reject at high speeds,with tyre(s) burst would be 100% overrun (did that in the sim also)
The oil from stby will return to tank B...hmm...not true
" A leak in system B does not affect the operation of the stby hyd sys" 13.20.3
Furthermore,the stby sys works with the stby rudder pcu,not the same one used by A or B sys.When in use ( flt control switch to stby rud) the related hyd sys shutoff valve will close,isolating the system.
So ,I suggest, you tell that TRE to review the hydraulics chapter as there've been some changes done.
windy: for tyre burst the 'book' recommends to stop if only bellow 80 kts .Above 80 you should stop for eng fire,failure,aircraft unable or unsafe to fly,predictive windshear.
The definition for unsafe it's a bit tricky.Actually,it gives you the option to reject a take-off due to any reason that you can qualify as an unsafe situation on your oppinion.