Kearny Fallout Meter (KFM)
Quote from one of the sites you listed: "In this manner dose rates from 30 mR/hr up to 43 R/hr can be determined with an accuracy of 25%."
I've built these for fun but realistically they are almost useless compared to a real Geiger counter and a few dosimeters. They are last resort if you have nothing else. To start off you need about 30mR/hr to even get a reading. How much radiation is that? Where I live (Next to a Nuclear Plant) background radiation is 100mR/Year. So to even get a reading you need 3/10th's of a year worth of radiation per hour to get a reading.
That's 2,628 times normal Radiation just to get a measurement.
Those soup can KFM's are sensitive to wind, shaking, rain, humidity, movement, static electricity and a host of other things. If the radiation climbs and the aluminum leaves collapse your out of luck because you have no idea of your total exposure.
Also with a soup can and its giant time delay. Can you find the spot with the lowest radiation in your home or neighborhood? It would take endless hours with a KFM. You can quickly map out the spot with the lowest radiation with a Geiger counter. Do you know if you're crapped up (Term for contaminated with Radioactive particles) with a KFM? Can you detect where the contamination is? Is it on your shoe or your hat? You just can't tell. I could go on forever on how impractical KFM's really are.
If you can't afford a Geiger counter you could buy a 200mR, 5R and 200R dosimeter and charger for about $50 total. You should have those anyway even with a Geiger counter. You could use them like a KFM and if a Nuke goes off you can look and immediately see your dosage. The 200mR and 5R can serve as a makeshift Geiger counter much better than a KFM. The 200R is for total dosage.