Ultimately, if anything useful is ever going to be done with this station, it will need a more powerful signal with nighttime service, which will involve a frequency change and construction of a new transmitter/antenna facility--not cheap, but it can be done--witness KGOW.
I just don't see it happening, ever. The only chance for real improvement that would still qualify as a minor change would be to move a few kilohertz either direction. 630 is out, along with 640 due to co-channel stations in San Antonio and Thibodaux LA, respectively; likewise with 660, of course, because of KSKY from Dallas. The only real possibility left is 670 but that would be a struggle, considering the need for adjacent channel protection to San Antonio on 680 and KSEV on 700. Even if daytime interference issues could be addressed it might take a separate nighttime site, and there's no guarantee that any kind of decent power could be licensed on that frequency, either for day or night operation.
I've worked on similar projects over the years and you reach the point pretty quickly where the cost of the undertaking eclipses any potential ROI. That's especially true these days when it's obvious that AM isn't going to be around that much longer. In my opinion, if this latest attempt to do something with KIKK doesn't succeed it could be time for them to cut their losses and turn in the license.