Easy solution here to a very vocal problem that should by the math at least appease both crowds... But probably won't.
Separate the lockouts, but per-boss only make a character eligible for loot and JP on one version of the raid per week.
That way the complainers have their raid flexibility. The people who don't want to be forced to run twice as often don't have to worry, because the impetus is not on them to try and gear up twice as fast. You can use 10-man for tactics and 25-man for loot runs... Whatever takes your fancy.
Suffice to say if you take the lockout out of the equation, anyone that has a material argument as to why you should be able to be rewarded twice really doesn't believe that players should be empowered to make a choice.
Nobody should have to be emotionally-blackmailed by overzealous guild/raid leaders into raids they don't want to do a second time every week.