777 Inflight autostart behaviour - Dual Eng Fail/Stall
I'm assuming you were in a GE powered model re the 270kts, Rollers being 250kts.
The inflight start envelope (above FL220-APU bleed not available) will only offer a windmill start unless bleed air is available from other engine(not in your case).
Once speed is reduced below 270kts GE ,250kts Rollers, you will notice a magenta XB OR XBLD ( depending on blockpoint) above the starting turbine, in your case the N2.
Once this is displayed the checklist will guide you to use bleed air to assist start.
I've seen what you describing before and it tends to happen because while actioning the checklist, when the statement, 'is XB or XBLD shown' the speed bubbles up and down a knot or 2 above 270GE/250RR hence no longer displaying XB/XBLD.
Everytime I've used this in the sim the relight/s have been text book.
In short if bleed air is available and a windmill start is not working , then change your plan. Just put the start selector in start and try that. Better than the inevitable dead stick forced lob.