Persistently or aggressively enabling Low Power Mode
Yes, the _CDBatterySaver API in the CoreDuet (Private*)Framework can be used to toggle low power mode.

An example invocation, untested:

#import &lt;CoreDuet/CoreDuet.h&gt;
#import &lt;objc/runtime.h&gt;

-(void)setLowPowerMode:(BOOL) isOn {
    _CDBatterySaver *batterySaver = [objc_getClass("_CDBatterySaver") batterySaver];
    int nextState;

    if(isOn) {
        nextState = 1;
    } else {
        nextState = 0;
    }

    if([batterySaver setMode:nextState]) {
        NSLog(@"Set power mode state");
    }
}


I'd wrap this in an app with a background task to watch for low power mode (both well documented APIs). This can be done with Xcode as Apple allow building and installation of apps to your phone without requiring a developer license (IIRC).

*See answer to question how to import private frameworks in xcode. Note: header files can be found on GitHub without the need for a jailbroken device.