Scrapped the analog design. Using a CD4541B programmable timer and external RC clock network (I can't find a clock IC low enough for a reasonable price), I think I have a device that works. Further on the bench testing is required. 

Updates: 

4/2/2021: Bench testing completed. 5 minute timer R_TC is 330 ohms, 2 hours is 9300 ohms. Began protoboard development. Difficulties with relay pin size resulted in undesired modifications. 

4/5/2021: Prototype build continued. 

4/6/2021: Removed IC mounting component from a previous timer and added to protoboard. Completed protoboard and began testing. 

4/7/2021: Protobard testing completed, things are working great. Need to adjust schematic to reflect component footprints.