The prospect can work if we admit that the system is small and then increase its efficiency towards outdoor use. Yeah, time to cheat.
1). Starting with the single 10" subwoofer which is the main limiting factor, dial its crossover up to terribly boomy, which is the only thing that will be effective to increase the output for distance impact outdoors. See also the Boominator thread on how to get significant bass outdoors with little 10" woofers.
2). And then see what size cap to put in series between the LM1875 amplifier and its speakers to block bass loading (conserve amp power) and the cap sized to match it up to the fairly high pitched subwoofer. Also consider reducing the input cap size on the LM1875 amplifier. Both input and output roll-offs may get you enough output power efficiency.
3). Now add a larger cap between the subwoofer's amplifier and 10" woofer to reduce X-max (if ported, then some port adjustment may be needed--shorter port tube). Also set your source EQ with the 50hz control down, not up. With only one modest woofer to use, try to block pitches lower than 90hz. If at first you don't succeed, seal off the port to Stop the X-max, fiddle the "conservation cap" size, and then eq the heck out of it. See also Bob Cordell's site on speaker bass.
Notes:
Small systems that succeed outdoors are usually unpleasant indoors and vice versa. See also room gain or cabin gain topics, which help bass and aren't present outdoors. If you want to use it outdoors, you'll probably have to tune it outdoors, well before the event. With just 1 of 10" woofer, you're going to have to maximize the output at the expense of the quality (due to the absence of the normal amount of woofers for outdoor PA).
Your system should be able to get the drum impact fairly well, but your bass guitarist will have to bring his own amp, hopefully equipped with something more significant than one modest woofer.
P.S.
See also SA Stereo Tool, a professional but free software that can be used for a boost and/or limit x-max, and well it might be quite useful. A small system converted for maximum outdoor output may not be very pretty, but you could possibly dial some pretty back in with SA Stereo Tool, if you have a rather quick laptop available. It may need the sound card software adjusted for input port type as some of them default to microphone but can be swapped to line in via the driver software. Some don't have line in at all and that would not be so handy. This all needs checked out before the event.
