Thanks to all for the suggetions. I ended up taking my pedal board and bass over to a friend's house to play some. Plugged into his bass rig and only used the factory presets which, as before, sounded fine (but no calibration response). A couple of days later and back home on my rig, I plugged in to give it another go. With no other changes and selecting some of the community patches which previously produced no calibration response, I began to see the red calibration light flash just after selecting the patch. Again, this was not happening previously. I could then get those patches which produced this response to calibrate according to the procedure in the manual. Not all, but some. Excitement ensued.
I borrowed a couple of compressor pedals (a Boss CS-3 and a super cheap Amuzik) and a bass to test. With either compressor in front of the C4, I was able to trigger the expected calibration response on most patches. Woot! The bass I borrowed, an Ibanez SR-300, produced a similar result without the comp. According to every source I can find, that bass is equipped with passive pickups. I'd say there's probably something to QM's suggestion regarding a preamp adding gain to account for low pickup output. I'd still like to be able to determine the reasons for these differences from one bass/preamp/pickup setup output to another, but I'll leave that for another time.
The Boss comp sounded like poopiee. The cheap Amuzik sounded great and cost a mere $19, so I purchased one for myself along with an Amuzik boost pedal (also $19). With just the boost in front of the C4, most patches trigger correctly. However, with boost>C4>comp, nearly every patch sounds superb. There are still certain users' patches which require me cranking the input gain and volume to open the filters, but at that volume they are way too loud for practicing at home without earplugs, so not particularly usable for me at the moment. fivestringgecko and thehook are two of the featured artists whose patches fall into this category for me. A bit of a shame since they've got so may excellent sounding patches, but it's not like there aren't a gazillion more great ones to choose from so no worries there. I'm curious to know if having a higher-powered amp and a bigger speaker cab will make for a smoother time exploring these sounds. Also would like to see how throwing a microthumpinator into the chain will impact the output. And then there's that Atlas purchase I've been considering which might confer superior compression options. I really don't know enough about how to implement compression, boost, or EQ to know where to go next, so still plenty to explore.
So, while I'm not particularly thrilled with the fact that I had to purchase more stuff to get this pedal to work with my (pretty standard) bass, I am thrilled that it is now working, and under $40 to dip my toes into pedals that I was looking to try out anyway isn't that big of a deal in the grand scheme of things. Thanks again for all of the positive input from the experienced users here. Looking forward to digging into patch creation to see what I can come up with.