I applaud your extra efforts to do the job well. I just think that doing this 'Off the books' so to speak clouds the real cost of the effort. I would much prefer to see the actual, real expenses accounted for and reimbursed. Only then can the true costs be compared against benefits/output. By this means society can both measure true performance and make informed decisions about the allocation of limited resources across numerous needs.
As a teacher, I don't even think we should get paid for our extra time. It is part of the job. I don't think all teachers spend hours upon hours extra, but there are lots that do and don't seek any recognition for it. Most states do give out some reimbursement, but it is limited, as it should be. What concerns me more as an educator is the hatefulness, complaining, negativity, etc. that some of the education liberals have developed against teachers. Those are the attitudes I see with anti-war protestors, anti-abortionists, etc. "Real" people should be above the name-calling. It's not something I try to teach my first grade students.
As you go on to point out, many teachers do not put forth the extra effort and both that fact and the fact of extra efforts going unrecorded and unrecognized in the system are a problem IMO. The failure to accurately and completely measure the inputs (Time, Money, Other resources) makes comparison of the outputs (Educated and socially adept adults in this instance) meaningless and/or subject to manipulation. The same is true of any activity, economic or otherwise.
IMO until the "True" costs of education are recognized, then any measurement of the performance of our educational institutions is meaningless and, in most cases, actually impedes the achievement of the goal of educational excellence.
So I say, monitor and pay all costs, compare the cost against established and agreed upon standards of measurement and let the dice fall where they may. Again, IMO to hide, or otherwise depend on the dedication of individuals to absorb, on their own, the costs of any activity only leads to inefficiency and disparities in the allocation of benefits from these activities.