Since your whole strategy is built around ramping up your beast with your economy, you need to make sure that it's actually able to swing.
The best way to do that is by making yourself more survivable and by helping your beast swing faster.
Scale Your Tankiness
Whether it's by Shielding, Healing, Health Stacking, or all of the above you need a way to protect your beast.
Pygmalien has a ton of these items, but one of the stand outs is the Lemonade Stand.
Since you're already buying and selling items, Lemonade Stand lets you double dip by scaling your Max Health when you sell Small items.
Another good option is the Belt, which gives you an instant flat +50% Max Health - very potent if you've already scaled a decent amount.
Decrease Your Cast Time
The other angle your supportive items should focus on is lowering the cooldown of your beast's cast - the faster the better.
This is because your biggest threats are the builds that can Freeze, Slow, or rush you down.
If you can get one swing off, you should be able to win your matchup since a lot of builds won't be able to survive your scaled damage.
These are options like Phonograph and Stained Glass Window which offer significant cooldown reduction.
You can also consider options that offer Charge and Haste, it's up to you and what you find during your run.
Skip Most Skills
Skills aren't as important compared to other builds since most of your gold is going to item stacks, but Big Guns is a really good one to look for if you're playing Beast of Burden .
If taking Skills is your best option at choice points, look for ones that help your econ, tankiness, and casting speed for your beast.