Sister 2x10 joist with a 2x8
The Code requires a minimum ceiling height of 7’-0” for habitable spaces, unless 1) it’s a slopped ceiling, 2) beams in ceilings 3) basement remodel, 4) bathroom or shower. 

1) Slopped ceilings shall have at least 50% with at least 7’ height and slope down to no more than 5’. 

2) Beams in ceilings spaces not less than 4’ on center, can drop down 6” below the 7’ ceiling. 

3) Basements can have 6’-8” ceilings in non-habitable spaces. 

4) Not more than 75% of a sloped ceiling in a bathroom can be less than 7’ if a space in front of toilet, sink, shower is 6’-4” high. 

Yes your 2x8’s at 16” on center spanning your maximum length of 11’ will be strong enough and comply with the structural code requirement of providing a minimum of 40 lbs. per square foot. (Sistering a joist to the original joists may be overkill.)

However, you have other issues regarding ceiling heights, exits, etc.