Here's the skinny on Greensburg from someone who used to live 30 miles east of there.
The big AM in Greensburg is KWLS 1290 out of Pratt. Their day (5KW) signal is directional west, and sends out a city grade signal about 50 miles to the west because of the high ground conductivity in that part of the country. The 0.5 mv signal goes to about Garden City. The 500 watt night pattern is a cloverleaf, and how well it can be received in Greensburg depends on weather and other factors (the further north you are, the better the signal). It may only be 500 watts, but I can tell you a lot of stations would kill to have the night coverage KWLS has, such as it is.
The other two close AM's to there are KGNO 1370 out of Dodge City, 5KW non directional day with a good signal coverage and 230 watts at night, also non-directional (and a class B); and KNNS 1510 from Larned, a daytimer at 1KW with 500 watts critical hours.
I think the religious station you mentioned is KKCV, which just went on the air in the past few weeks. It's part of the Bott network out of Kansas City. There are a number of FM signals out there that the maps may not show reaching Greensburg but because of that legendary flat terrain do. That would include the three commercial FM's in Dodge City (all sister stations of KGNO), at least one of the Garden City based FM's plus single stations from Great Bend and Hutchinson (the latter a C0 on a Pratt License). There is also another religious station out of Medicine Lodge (locally programmed) that can be heard there, and there's a translator in the county for a big CCM station based in Meade (also locally programmed).
I don't know what the stations out there did Friday night, but the Wichita TV stations were on top of the storms all night. (The TV market covers about the western 2/3rds of the state) Most everyone there has cable, and can get at least two of the major networks over the air, depending on how big an antenna they have.
NOAA weather radio has a transmitter in Kiowa County.
I do know there has been some talk off and on about trying to improve nighttime radio reception in that part of the state.