a) I did make a mistake, when i ran it again, i got the same answer than you.
Keep in mind that if the time units of the process is given in minutes, the time units of the controller is also minutes and NOT seconds.
I am not claiming that this controller is the best you'll get, but what i do claim is that, provided that the process parameters do not change and there are not significant other disturbances, a PID controller with tuning constants of: gain = 0.15 and integral time constant = 2.87 minutes, will do a reasonable job of controlling a pure 10 minutes dead time process with a process gain of 1.
b) For a process with a high dead time to lag ratio (like yours), any model based control algorithm can give significant better performance than a PID controller, in terms of stability, tracking and robustness. Common examples of model based algorithms are the Smith-predictor (dating from the 1950's), Internal Model Control (IMC) and Model Predictive Control (MPC). I have had good real plant success in both Smith-predictor and MPC.
There are undoubtedly other algorithms that can also beat a PID controller.
Do you mind sharing more information on your algorithm? Maybe others can also learn from your experience.