How should I go about sourcing for a packaging company or finding ...

Shipping components are expensive and unless you have the volume to buy in quantity vs small bundles is when you'll be able to shop around for a better deal. For example, Uline offers packaging in bundles of 8 or 25 as their minimum, this is stock item for which they order several thousands units of to keep the cost down. For you it fits because you can buy in small amounts at a time. However, if you have a need for at least or more units then buying from Uline is really expensive compared to what you could buy them for. Uline is a major distributor with a 45-50% markup on their items (give or take) as they have large warehousing and infrastructures. If you are ready to move to the next level, first find the correct material name for each packaging component, and look for suppliers of that particular item. Search websites likehttp://www.thomasnet.com/ for suppliers. Or go through a packaging broker instead of a distributor, like Landsberg Orora, or Ernest Packaging, and they can do all the leg work for you and still save money.
Additionally, I know your drawing is not to scale, but there seems to be excess empty air space, if that is true then you can customize your packaging per exactly your needs, which will help to further bring the cost down. An engineer should take a look at your current situation because there is more at play than just shipping components - method of shipping, weight, weather condition, materials thickness etc all play a roll and can all contribute to cost saving while making the whole thing function better.
This question is common enough that I've written tutorials on it http://howtobuypackaging.com/how-to-buy-packaging-part-1-determining-your-packaging-needs/.

You can find more information on our web, so please take a look.

Choosing packaging suppliers doesn’t have to be a major headache.

All you have to do is narrow down the list of key attributes that you’re looking for in a supplier then measure your candidates against that list. 

To help you, we’ve created a list of six factors to look for in a packaging supplier. 

1. Do They Keep Enough Stock?

Make sure that your supplier keeps a reasonable amount of stock on hand so that they can deliver to you on time.

Some suppliers may not have the room to house much stock. Therefore, when their customers place orders, there can be a significant lag between the request and the delivery. The problem often increases around major holidays. 

2. Do They Deliver Supplies on Time? 

Your supplier can have the nicest sales rep, the fanciest website, and the lowest prices, but none of that is of much use to you if you can’t count on receiving your supplies on time. The supplier may have in stock the items that you’ve ordered, but yet delay delivering them. 

You should only choose a supplier with an established track record of meeting deadlines. Their sales rep may try to reassure you that their previous delivery kinks have all been ironed out, but don’t take her word for it. If their latest online reviews still highlight tardiness, watch out.

3. Do They Use Quality Materials? 

If you have unusual demands for your packaging supplies, you may need to perform a greater level of research than average to find the supplier that’s right for you. 

You will get efficient and thoughtful service from Yifu Packaging.

Even if your packaging needs are rather typical for your industry, you should still be particular about the quality of the packaging materials that are used. Make sure that the supplier’s goods exceed or at least meet the industry standards. 

4. What’s Their Level of Customer Service?

The sales rep assigned to you is your key to understanding the supplier. How well-trained does the sales rep appear to be? That’s an indication of the level of professionalism that’s common to the supplier. 

You want a sales rep who thoroughly knows her company’s products. She should be able to tell you which product will work best for you and why. 

You also want a sales rep who’s friendly and personable. There’s no sense in establishing a working relationship with someone with whom you don’t communicate well.  

5. Are Their Prices Competitive?

You want to find supplies that have a reasonable cost, but you shouldn’t always go with the cheapest supplier. You may be sacrificing quality.  

For example, the discount supplier may not have the staff to reply to your questions in a timely manner. That same supplier may also cut corners in other aspects of its operations that could end up costing you in the long run. Cheap supplies can come back to haunt you if your customers complain about your product packaging.

6. Do They Offer Customization?

If you want to stand out from the crowd with your style of packaging, choose a supplier who can work with you to create unique packaging. Your packaging is part of your brand awareness. 

Do the companies that you’re vetting have graphic design capability? Do they have experience helping companies create branded packaging?

Are You Ready to Start Choosing Packaging Suppliers? 

Now that you’ve read our opinion of the six factors to look for in packaging suppliers, it’s time for you to start doing your research.

If you want to learn more, please visit our website Custom Packaging Supplier(de,ru,fr).