Tests order dependency due to constant (final) fields

What is the recommended pattern to modify constants for unit tests? This is currently what I've used for some time and today I realized it's flawed.

Assume my class looks like this

class Foo {
   private static final int MAX_TIME = Integer.getInteger("myProp", 1000);
   ...
}

The fact that I use a VM property is not only to modify it in a unit test. It is because I want it to be immutable from the actual code and I don't want to pollute a constructor with it since it is an implementation detail.

So, in production I want a timeout of 1 second; however that's too long for unit tests so I do this

class FooTest {
   @Before
   public void setUp() {
      System.setProperty("myProp", "50");
   }
   @Test
   public void testThatAssumesTimeoutOf50() { ... }
}

This worked fine for a long time until today I finally added a BarTest like this

class BarTest {
   Foo mockFoo = mock(Foo.class); //actually done in a @Before method in the real code
}

Now what this created is that my tests fail or pass depending on the order of execution. If Foo is tested first, the test that assumes a testing timeout of 50ms passes. But if Bar is tested first then this makes Foo to be loaded due to the mock so MAX_TIME takes the default value of 1000 and then when BarTest ends and FooTest starts, the test that assumes a testing timeout of 50ms now fails.