React navigation + react hooks problem with callback param

App.js

import React from 'react';
import {
    createAppContainer,
    createStackNavigator
} from 'react-navigation'
import TestScreen, {
  testScreenOptions
} from './TestScreen'

const stack = createStackNavigator({
    Test: {
        screen: TestScreen,
        navigationOptions: testScreenOptions
    }  
})

const Navigator = createAppContainer(stack)

export default () => <Navigator />

package.json

{
  "dependencies": {
    "react-native": "0.59.2",
    "react": "16.8.3",
    "react-navigation": "3.5.1"
  }
}

TestScreen.js

import React, { useEffect, useState } from 'react';
import { Button, Text, View, StyleSheet, Image } from 'react-native';

let renderCount = 0

const TestScreen = (params) => {
  const [fieldValue, setFieldValue] = useState('')

  const handlePress = () => {
    console.log(fieldValue)
    
    // handlePress.value always 1 here
    setFieldValue('' + handlePress.value)
  }
  
  handlePress.value = renderCount++

  // Here we do a setParams to expose our callback
  useEffect(() => {
    params.navigation.setParams({ handlePress })
  }, [fieldValue]) 
  // if we add [fieldValue] as a dependency here,
  // react will update the lambda and everything works.
  // But this forces us to reference all 
  // used params in the handlePress.. which is
  // EASY to miss and causes bugs that are HARD to find.

  // Basically, every function used in the setParams
  // should be pure to avoid reference/leak problems

  return (
    <View style={styles.container}>
      <Text style={styles.paragraph}>
        value: {fieldValue}
      </Text>
    </View>
  );
}

const styles = StyleSheet.create({
  container: {
    alignItems: 'center',
    justifyContent: 'center',
    padding: 24,
  },
  paragraph: {
    margin: 24,
    marginTop: 0,
    fontSize: 14,
    fontWeight: 'bold',
    textAlign: 'center',
  }
});

export const testScreenOptions = ({ navigation }) => ({
    headerTitle: 'Test',
    headerRight: (
        <Button
            mode='text'
            onPress={ navigation.getParam('handlePress') }>
            Press me
        </Button>
    )
})

export default TestScreen