Strange Slant 6

A gallon of oil in 15 miles could not have gone out the tail-pipe without smoking the whole neighborhood. Since you didn't see it leak out, it must still be in the engine. If not in the oil pan, it must be in the top. Another guy had a similar issue and found clogged drain holes (beside lifters). Seems an engine must be extremely gunky to do that, and even stranger in a slant where you need to remove the valve cover every few years to adjust the valves. Of course, yours could be a later hydraulic cam since we don't know what car or year.