I have done a little research into this question, attempting to find some data for my master's thesis (longer ago than I care to admit). I found very little (though more may have come out since then), aside from serious analysis of a system called "block scheduling." Block scheduling attempted to emphasize various subjects by altering the both frequency and the duration - more time on fewer days. Thus, English and History would get twice as much time on alternate days, while Math and Science would get the same, etc.
I attempted to make this case for a school I was working in at the time, which flipped the times of Judaic and secular studies in the later grades. This school had the 9th and 10th grades in Judaic studies in the morning, and secular studies in the afternoon. Then, the 11th and 12th grades had 1 period of Judaic studies in the morning (to accommodate R' Moshe's issue), then the entire slew of secular studies, then the remainder of their Judaic studies. This also allowed most teachers to be employed full time - their classes were spread through different grades and time slots. I don't know how easy this made life for the principal (I do know that scheduling was a nightmare), but perhaps some combination of the two tactics can be used to satisfy your problem.
In any case, I would suggest that no message about the primacy of Torah or anything of that kind will make it to the kids if it is not at some point explicitly expressed. Our students are smart; trusting them to pick up on a philosophical point based on the timing of the bells in the morning is a little much. That can be one part of a larger, integrated philosophical approach that the school is taking, but it must be made clear, and expressed often by the faculty, if you want your students to grasp its necessity.
If anyone is doing serious research on this topic, or knows of research, I would appreciate being informed. I am currently looking into doctoral thesis topics and am mostly interested in conflicts between Judaic and secular studies at the administrative level.
