<<And you don't think spoiler drag is a big problem on take off?>>
No. I am on simulator training for the 737 now. We measured time and distance from Vmo to 220 kts speedbrakes retracted and fully extended. Distances 14/10 miles. They only made 4 miles difference and 20 seconds in the time to slow down. The 737 speedbrakes fully extended are not very effective at high speed. The effect of the speedbrakes is not great, and that is with 3 raised on each wing. Using them as spoilers to assist the aileron, 2 will rise on one wing only. How effective at creating drag in the few seconds up to 150 kts do you think 2 spoilers will be? On all the jets I've flown, with a strong crosswind on takeoff, I've needed far more than 10 degrees aileron control. The maximum I recall ever seeing is about 45 degrees, and I've never run off the end yet! It's a fact of life, you need it. Your quotation from the manual says <<limit control wheel input to that required to keep wings level>>. It does not say to limit it to avoid spoiler upfloat. the meaning is to 'avoid excessive control wheel.....blah blah'. This is in keeping with my previous experience which is 8 years 737 as well as 18 years 747.
Incidently, aileron over 10 degrees will raise the spoilers according to the Tech manual.