Your understanding matches mine, at least.

Is your sub powered, or do you have a separate amp driving it? Generally powered subs include a low-pass crossover that would work well for these purposes. There are external products that will do it, too, such as the Outlaw ICBM (which provides 6.1 analog bass management) and the Paradigm X-30 (better suited to this case), but it may not be necessary.