Hi Eric,
You did come to the right place to ask your question, however based on the information you have given it is a little hard to say for sure that we can accomodate for what you are looking for. In terms of screen customization, from what you mentioned, I believe it would be possible to customize the screens as you are requesting. For example you can have a screen that would show a grid similar to what you provided above, giving the Line Time and Time Loaded fields as time/date stamps. You would have the ability to add custom fields in Method that could include any of these fields not already offered in the stock Table. Color could be a text field or even a dropdown field, if you are working with a select amount of colors. You could also attach timers to a your custom screens, which sounds like it would be required in your setup. When you start the Timer, it would create a value for the "Time Loaded" field, then when you stop the timer it could internally calculate "Line Time" based off an internal Math Calculation.
In terms of creating schedules, again this is bit hard to answer without more details. However if you are setup with a Gmail Enterprise Account, then depending on how you this setup, you should have access to your employee's Google Calendar, and appointments can be setup through this. You could also share a Calendar that would show all apointments/tasks/activites linked to this calendar, for 1 or all users to see, again depending on your setup.
We do offer a 30-day free trial for Method, which gives you access to all advanced features. I would suggest if you have the time to try this out, you can also take advantage of our Webinar Videos that discuss some higher levels of Customization that can be done on the Method Screens. I hope this helps, if you still have more questions, please do not hesitate to ask them here.
-Ben