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I believe these are the things you need to consider or do:
1. First, make sure to set your "Clear Hidden Field Values" to "Clear on Being Hidden".
This means if your drop down fields for the selection of speaker are hidden, then the values on it automatically resets or being cleared, which should also mean that the conditional logic tied on them should not work.
2. Now avoid setting conflicting conditions. Example:
IF "Thursday" is EQUAL TO "Bobby Jindal" THEN
SHOW "Bobby Jindal"
HIDE "Ben Carson"
This will cause you problems because I presume you already have another condition to where you want to display "Ben Carson".
The trick is this, when a "SHOW" action is NOT TRUE, then it automatically HIDES the said field. Meaning no need to setup a "HIDE" action. On our example above, you can just write it like this:
IF "Thursday" Is EQUAL TO "Bobby Jindal" THEN
SHOW "Bobby Jindal"
No need to hide "Ben Carson".
3. Now I see you have a lot of fields per speaker, the best way to show them per group is by wrapping them in a form collapse tool. Here's a specific guide that will help you: https://www.jotform.com/help/297-Show-or-Hide-multiple-fields-at-once-using-form-collapse-tool
In your case, here's how I setup my cloned form:
I wrapped the section of Ben Carson with a form collapse field and named it "Ben Carson Section".
I did the same with Bobby Jindal, and named the form collapse of it to "Bobby Jindal Section". Now do the same with the other speakers you will be setting up.
After that, we will need to create conditional logic for this (make sure to remove the previous ones to avoid conflict). Here's my two conditional logic for the two speakers. Instead of selecting multiple fields to show, we just need to select the form collapse for each section.
Here's my cloned form with all the changes above: https://form.jotform.com/61549173203957. See if that's how you are expecting it to work. You can clone my form to have a version of it in your account: https://www.jotform.com/help/42-How-to-clone-an-existing-form-from-a-URL
Let us know if you need more help on this.