The post in question ’30-sbd-webgl-screen-capture-contest’ has 119 reblogs.

Full results as json in this gist.

Node.js example tested and working using SteemSQL database (you will need a user/pass see below)

const sql = require('mssql');

const config = {
    user: 'username',
    password: 'password',
    server: 'vip.steemsql.com',
    database: 'DBSteem',
}

sql.connect(config).then(pool => {
    return pool.request()
    .query("SELECT dbo.Reblogs.* FROM dbo.Reblogs WHERE permlink = '30-sbd-webgl-screen-capture-contest'")
}).then(result => {
    console.dir(result)
})

sql.on('error', err => {
})

Result will contain an array with all of the accounts who reblogged you and the timestamp of the reblog.

Explanation

Unfortunately Re-blogs are not stored on the post that has been re-blogged :(. I'm not sure why but you're right reblogged_by will always be empty. I know, it seems a bit ridiculous.

Reblogs are created as custom json and broadcast to the network like so -

let ACCOUNT_NAME = ‘’
let ACCOUNT_KEY = ‘’
const json = JSON.stringify(['reblog', {
  account: ACCOUNT_NAME,
  author: ‘money-dreamer’,
  permlink: '10-sbd-steemjs-programming-question'
}]);

steem.broadcast.customJson( ACCOUNT_KEY, [], [ACCOUNT_NAME], 'follow', json, function(err, result) {
    console.log(err, result);
});

Unfortunately like you’ve found there is almost zero information about reblog on the steem-js library. You can not get reblog directly from the API but there is still hope.

The options

a) Create your own record of transactions. Stream block operations as they come in and database them. You can then search where there is a custom json transaction that matches your name/permlink. You’ll need to retrospectively go through each Steem block and database the transactions to get a complete set of data.

b) Use a third party set of data. Steemsql and steemdata are two that I know of. The bad news is that steemdata looks like it’s currently down (just tried connecting to the db, no good and the web api is not responding). Steemsql is now a subscription service costing 10SBD a month or 1SBD a day. https://sql.steemhelpers.com/ was exactly what you needed but is also currently down :(.

Results/What I did

I signed up to the SteemSQL service on the 1day plan to test my theory for you. I used Navicat SQL explorer at first to explore the SQL Databse and there is a helpful reblog table setup to save having to search through all json transactions.

The example I created uses mssql npm package to connect to the sql server. You’ll need a username and password by subscribing to steemsql for a day or month.

p.s thanks to @arcange who runs SteemSQL and helped me get the Database setup when I couldn't connect.