Starting with the stator of a known billiard table frequently turns out to quite easily generate it. Some other rotors frequently turn up elsewhere as well (cuphook, Gray counter, R2D2, burloaferimeter, and the 4-cell babbling brooks in particular).
For now, six discoveries in the p3 to p5 range I'm not seeing in the DRH collection (though some of them look deceivingly simple?):
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x = 83, y = 15, rule = B3/S23 76b2o$74bo2bo$9bo18b2o44b3o$bo3b2obobo6b2o10bo$obobobobobo5bo2bo7bo4bo 8b2o4b2ob2o5bobo12b7o$b2obo3b2o5bobo2bo5bob5o8bo6bob2o5b2obob2o7bo4bo 2bo$3bob2o8bob4o5bo11b2obo6bo11bobo5bo2bob2o3b2o2bo$3bo4b2o2b2obobo5b 2obobob3o5bob2ob2obobo8b2obobo5b3o6bo2b3o$2obobo3bo2bo2b6o2bobo7bobo7b obobo9bo2bobob2o5b4o3b2o$2obob4o5bo5bo5b3obobob2o7bob2o6b2o3bo3bob2o4b o9bo$4bo10b5o12bo11bo8bo2bobo3bo8b9o$6bo10bo8b5obo9bobo10b2obobobo$5b 2o19bo4bo10b2o15bobo11b2ob2o$29bo30bo12b2ob2o$29b2o!