Use https://github.com/voceconnect/wp-large-options/ as storage for specific widget types

wlo-widget.php

<?php
// Plugin Name: WLO Widget

// register core 'text' widget
register_wlo_widget( 'text' ); // id base

/**
 * hook in
 */
function register_wlo_widget( $widget_id ) {
	add_filter( 'pre_option_widget_' . $widget_id,        'wlow_defer_to_wlo_get',    10, 3 );
	add_filter( 'pre_update_option_widget_' . $widget_id, 'wlow_defer_to_wlo_update', 10, 3 );
	add_action( 'update_option_widget_' . $widget_id,     'wlow_clean_up_option',     10, 3 );
}

/**
 * get the option from wlo if possible
 */
function wlow_defer_to_wlo_get( $false, $option, $default ) {
	$wlo = wlo_get_option( $option, $default );
	if ( $wlo ) {
		return $wlo;
	}
	return $false;
}

/**
 * update wlo
 */
function wlow_defer_to_wlo_update( $value, $old_value, $option ) {
	wlo_update_option( $option, $value );
	return $value;
}

/**
 * clean up original option.
 * we cannot short-circuit the update call directly
 */
function wlow_clean_up_option( $old_value, $value, $option ) {
	delete_option( $option );
}