Custom Rule to ADD a record?

Interestingly enough, I recently had a kinda similar use case. I typically try to stick with the auto-incrementing primary keys instead of altering the key field (e.g. to a User) for reasons I won't explain here. Anyway, it sounds like you could potentially leverage your existing Employees table in combination with Formula Queries and (conditional) Formula URL buttons to create a "Person Locator Service" or "Person Authorization Service." For example,

// _DBID_EMPLOYEES
// FID 3:    Record ID# (Integer)
// FID 999:  Quickbase User (User)
// FID 9999: Quickbase User Has xyz Permission (Checkbox)

// Return the Current User's Record ID
var Text QueryResults = ToText(GetFieldValues(GetRecords("{999.TV.'" & UserToId(User()) & "'}", [_DBID_EMPLOYEES]), 3));
ToNumber($QueryResults)

Instead of returning the Current User's Record ID (3 in the above example), you'd could return a boolean of whether the Employee has access to perform the given operation (e.g. Add the record). Maybe something like:

var Bool HasPermission = ToText(GetFieldValues(GetRecords("{999.TV.'" & UserToId(User()) & "'}", [_DBID_EMPLOYEES]), 9999));

Then, in a Formula URL (button) you can conditionally show or hide the button based on the results of the Formula Query.

var Text UrlAddRecord =
    // Show form to create a new record
    URLRoot() & "db/" & [_DBID_THINGS] & "?a=API_GenAddRecordForm"

    // Set field value
    & "&_fid_xyz=" & URLEncode ([…])

    // Return to the context where this button was clicked
    & "&z=" & Rurl();

If (
    // Conditionally display this button
    $HasPermission = true, $UrlAddRecord,

    // Default to hidden button
    null
)

I'm not saying any of this is a good idea, but it is interesting and sort of allows us to extend basic User info similar to a User Profile in other web apps. I'd consider building a playground Quickbase app to test the ideas before integrating it into your production app.

The simpler version of all this would be to hardcode the allowable list of Users into a variable and then conditionally show the button if the current User is in the list.

Use care with Formula Queries too, especially because they likely cause n + 1 query issues that I don't recall reading about yet!

I'd also suggest really digging into why Quickbase's native Permission system doesn't accomplish what you are hoping to achieve.