Great work, could get any range you like (up to about 12') with an Arduino ultrasonic sensor setup. Recommend the Nano Every--not the Nano because it's a pain to work with--the Nano Every is about $10USD (buy with pins already soldered on, it's worth the dollar or so extra). Six wires total, (four for sensor, two for digital trigger pin out) to your solid state relay. Power the Every with a cell phone battery backup charger (USB to micro-USB)
Pack of five HC-SR04 sensors $14CAD on Amazon, c/w Dupont wires and mounting brackets(but also order a pack of female-female Dupont wires since the sensors and boards are both male, the extensions will come in handy though, another 10 bucks or so). That's 80 bucks roughly for 5 Nano Everys, 5 sensors, the wires and sensor mounting brackets. Not too bad.