Yes, smaller will work. The 16qt is the same diameter, half the height (holds half as many jars per run as well), and generally goes for the same price as the 23qt .
They also make smaller pressure cookers (not canners). The USDA tells you not to use the small ones for canning food. Something about the lack of thermal mass makes for shorter heat up, and cool down cycles, so target temps might not hold for the proper amount of time if you run it for the same duration at pressure as that established for larger pressure canners .... blaw, blaw, blaw..
I wouldn't use the small ones to can food, but for mushroom hobby purposes I think they are ok, though I think you will want a larger one soon. That's a long cycle time for less the 4 jars. On the bright side, an 8qt aluminum pressure canner can be had from amazon for about $35.