Has anyone experienced similar widespread GPS problems? Yes. Almost weekly
Are there any known systemic issues affecting GPS across multiple device types and carriers? Not that we've found. Every time we contact intuit, they blame our phone, or the cell towers or the location. 
Can anyone suggest advanced troubleshooting steps or diagnostic tools we haven't considered? Countless reports on the phone to the intuit people without a single response. EVER. 
Has anyone found a solution to comparable GPS problems? No. If you'd let me know of any, please let me know! 
Any help or direction would be greatly appreciated. We rely heavily on GPS functionality, and these ongoing issues are significantly impacting our daily operations. My opinion? Find another app. Tsheets was amazing right up until intuit bought them out. Payroll is a nightmare; if I owned the company I work for, I'd have left long ago. 

Sorry I cannot be of any actual help.