Parameters don't have the same functionality as filters meaning the 'only relevant values' doesn't work. You can always display a small info table above or below the parameters informing the user of the dates relevant to each university, meaning if they pick something not applicabale and get silly results it is explained.
If you don't like the format of the parameter change it to a string. That means you'll need to alter your calculated field to convert it back to an integer. Wrap the parameter name in the INT() function in your calculated field.
This is definitely closer to the ideal than I ever would've gotten on my own! It isn't exactly what I want, but I don't think Tableau has the requisite capabilities for a multi-slider that stops expanding before the range does but can then be moved within the range at that maxed expansion value. Thanks!
Quite late and I'm not sure I understand your request correctly or not, but anyways..
You can set filter as "max" date or "min" date whichever you prefer.
Then Put it as "Context Filter"
Context filter can limit LOD calc (Min) to pick up only minus 10 years from filtered Date.
Then add formula to limit to 10 years from set latest date.
And put this field on filter with choosing "True"
You can use Min and Max combination oppositely.
I really like this version, except that the start year on the filter doesn't change with the Max calculation. I am going to stick with the dual parameter method for now. Thanks!