Product Variations

I see what you want to do. If I were you I would :
First, rewrite the whole show file of the product view to display the main product information ( in $this->element ) and each variant information ( a foreach on $this->element->variants ). Then, add standard joomla panes around the variants.
Then, around all this, add the form like on the current show with a standard input button for the add to cart button.
And for each variant's checkbox, use data[<?php echo $row->product_id;?>] as name of the input checkboxes so that the system will handle adding several variants at a time in the basket (like we do on the cart file).

The easiest would be to use normal products and just define a custom function to handle the output of the characteristics with tabs for the first characteristic and radio for the other ones which will be in the tabs.

We will add the code below on our end in the file administrator/components/com_hikashop/types/characteristic.php :
$app =& JFactory::getApplication();
$chromePath = JPATH_THEMES.DS.$app->getTemplate().DS.'html'.DS.'hikashop_characteristics.php';
if (file_exists($chromePath)){
require_once ($chromePath);
if(function_exists('hikashop_characteristics_html')){
$html = hikashop_characteristics_html($element,$params);
}
}
if(empty($html)){


before:
switch($params->get('characteristic_display')){

and add a bracket at the end of the switch.

You should make the same modification and then create the file templates/YOUR_TEMPLATE/html/hikashop_characteristics.php where you can define the function hikashop_characteristics_html(&$element,&$params) which will return the html of the tabs. You can use the other cases in the function displayFE as examples of how to parse the characteristic data in order to build your HTML.

I'm not familiar with this extension but you should put your code in the function hikashop_characteristics_html since that's where you want to use it.

PS: I've updated the override code with a working version.