Creating dynamic controllers for the same route

As you already imply in your question, you'll want to use a custom controller action that returns the form depending on your node type.

First, alter the route to point to a controller method:

my_node_action.go:
  path: '/node/{node}/go'
  defaults:
    _title_callback: '\Drupal\my_node_action\Controller\GoController::goFormTitle'
    _controller: '\Drupal\my_node_action\Controller\GoController::goForm'
  options:
    parameters:
      node:
        type: entity:node
  requirements:
    _user_is_logged_in: 'TRUE'

Then you create the GoController.php file in your module's src/Controller folder:

<?php

namespace Drupal\my_node_action\Controller;

use Drupal\Core\Controller\ControllerBase;
use Drupal\Core\DependencyInjection\ContainerInjectionInterface;
use Drupal\Core\Form\FormBuilderInterface;
use Drupal\node\NodeInterface;
use Symfony\Component\DependencyInjection\ContainerInterface;

class GoController extends ControllerBase implements ContainerInjectionInterface {

  /**
   * Constructs a GoController instance.
   *
   * @param \Drupal\Core\Form\FormBuilderInterface $form_builder
   *   The form builder.
   */
  public function __construct(
    FormBuilderInterface $form_builder
  ) {
    $this->formBuilder = $form_builder;
  }

  /**
   * {@inheritdoc}
   */
  public static function create(ContainerInterface $container) {
    return new static(
      $container->get('form_builder')
    );
  }

  /**
   * Return the go form.
   *
   * @param \Drupal\node\NodeInterface $node
   *   The node.
   *
   * @return array
   *   Form render array for the go form.
   */
  public function goForm(NodeInterface $node) {
    $form = [];

    switch ($node->getType()) {
      case 'type1':
        $form = $this->formBuilder()->getForm('Drupal\my_node_action\Form\NodeType1Go', $node);
        break;

      // Further types/forms and/or a default form here...
    }
    
    return $form;
  }

  /**
   * Return the go form title.
   *
   * @param \Drupal\node\NodeInterface $node
   *   The node.
   *
   * @return string
   *   Form title.
   */
  public function goFormTitle(NodeInterface $node) {
    // Whatever logic may apply here...
  }

}