My FC gave up on the "Static" idea for the very reasons listed in the OP. We have to many people that can't play several times a week. As such, we switched over to doing signups for raids so those who are available on a given night can express interest. We can still raid 3 times a week, we just can't promise it will always be the same makeup. This does slow our progression, but it assures that those like the OP who have 1 - 2 nights a week are still able to learn the content. For those of us who make every raid, it takes a bit more patience, as we are regularly dealing with people learning on content that we already have down, however it is worth it to us.

The worst part about all of this is, while it is doable for someone like the OP to set up their own groups, that takes a lot of time. The whole reason the OP is in this position is because they don't have that kind of time. Those with the time are usually clearing current content each week, but that results in a weekly lockout that removes them from the pool of available bodies for those in the position that the OP is in. Thankfully the devs have now grasped this and will be fixing it in 3.0, but that is 6ish months away and so we will have one more round of people left behind.