Nginx as s3 proxy with private buckets

I'm trying to set up Nginx as a proxy for a static html/js webapp hosted on S3.
I read a lots of tutorials and posts and I could make it work if my bucket is set as public.

The reason I need Nginx as a proxy is that I don't want my bucket to be public.

Following this guide, I added the set-misc-nginx-module from this GitHub repo. The extra module, by providing AWS key and AWS secret, builds the authenticated S3 requests for each object of the bucket.

I recompiled Nginx and I managed to allow it to access to the protected bucket.
The problem is that I cannot render the html, and basically I'm being served with the xml content of the bucket I'm trying to proxy.

This is the configuration file of Nginx

server {
    listen 80;
    server_name [MY_DNS];

location * {
    set $bucket           '[MY_BUCKET]';
    set $aws_access       '[MY_AWS_KEY]';
    set $aws_secret       '[MY_AWS_SECRET]';
    set $url_full         "$1";
    set_by_lua $now       "return ngx.cookie_time(ngx.time())";
    set $string_to_sign   "$request_method\n\n\n\nx-amz-date:${now}\n/$bucket/$url_full";
    set_hmac_sha1          $aws_signature $aws_secret $string_to_sign;
    set_encode_base64      $aws_signature $aws_signature;
    resolver               172.31.0.2 valid=300s;
    resolver_timeout       10s;
    proxy_http_version     1.1;
    proxy_set_header       Host $bucket.s3.amazonaws.com;
    proxy_set_header       x-amz-date $now;
    proxy_set_header       Authorization "AWS $aws_access:$aws_signature";
    proxy_buffering        off;
    proxy_intercept_errors on;
    rewrite .* /$url_full break;
    proxy_pass             http://s3.amazonaws.com;
}

auth_basic "Restricted";
    auth_basic_user_file /etc/nginx/.htpasswd;

}

And this is the result if I try to access to my website

<ListBucketResult>
    <Name>[MY_BUCKET]</Name>
    <Prefix />
    <Marker />
    <MaxKeys>1000</MaxKeys>
    <IsTruncated>false</IsTruncated>
    <Contents>
        <Key>index.html</Key>
        <LastModified>[LAST_MODIFIED]</LastModified>
        <ETag>[ETAG]</ETag>
        <Size>22</Size>
        <Owner>
            <ID>[OWNER_ID]
            </ID>
            <DisplayName>[NAME]</DisplayName>
        </Owner>
        <StorageClass>STANDARD</StorageClass>
    </Contents>
</ListBucketResult>

**EDIT:**The index.html does have the content type set as text/html.

Probably I'm missing something in the Nginx configuration.

All works fine if I set the entire bucket as public and if I use the "simple" proxy approach.