What we do know is that in normal airline ops, performance software optimises as much as it can and on this length of runway it normally ends up as a balanced field. Also remember that TODA can include clearway, which is beyond the end of the paved surface, so your 35’ will not necessarily be achieved at that point OEI (but it will by the end of the clearway).
If you are planning balanced field, as most Boeing stuff seems to do, you are assuming TODA=ASDA (or usually TORA=TODA=ASDA). There being no stopway at Bristol your second sentence falls away, it can't be both balanced field and take account of a clearway that makes TODA longer than ASDA.
As per many preceding posts, we do know that OEI the average aircraft should make 35ft at the end of TORA/TODA/ASDA if field length limited, either naturally or by dint of flex. This assumes an engine fail at VEF, one second minimum recognition time with less than full thrust, then V1, then accelerate at 50% thrust to VR, rotate, and climb to 35ft at 50% thrust. The quoted figures of being at 150ft at the equivalent point having not lost an engine don't seem unreasonable.
Herod, check out the Delta DC10 crash at Chicago for the result of reducing speed in the climb after engine failure. Best angle of climb speed is close to V2+10, if you have achieved that nothing is gained by flying slower.