Here are some ideas:
Run either one of your searches from the Search window, interactively. When it completes, take a look at the Search Job Inspector. This will give you some information about how long the search runs, which may help you figure out how to do it more efficiently. More info about the Search Job Inspector is here.
The append command will run by default for only 60 seconds. You might need to increase that by using the maxtime option. Here is the link to the manual entry for append.
I would consider using post-process in your dashboard. Using this technique, you run one base search that collects all the data and computes all the statistics. The each panel displays the appropriate statistics, computed from the base search. This technique can be used in a variety of situations, but I think it is particularly appropriate here. This is discussed in the documentation under Use one search for a whole view. However, I think you should also download and install the Splunk Dashboard Examples app. You don't need to install it in production, just somewhere where you can review and learn from the examples; it's a very practical and useful resources.
HTH
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