Hi Scott;
Welcome to Permies! And welcome on your journey to becoming a rocket scientist! Now that you have the bug you won't be able to go back!
Lets start by asking if you own a copy of the "Buiders guide" written by Ernie & Erica Wisner. Readily available on Amazon or from them directly. This is the go to book for all new builders and accomplished builders.
The Wisners have over a 1000 rmh builds across the country. This book is worth every penny!
Ok, you built up a firebrick core, and it works great. Now you want to add your barrel. A barrel with a removable lid
should always have that lid on top. You need to see how your riser is working and how much ash might be building up. Putting on the barrel with the lid down is not a good idea, you would need to lift it off every time to see anything. Your barrel should have the bottom cut out leaving the lid to be on top.
When you add the barrel to a RMH you are creating the start of your "horizontal transition area" This area MUST be large
enough!!! I can't stress that enough! Many new builds do not perform as expected by this area being to tight. Bigger is better!
There are a couple of ways to start the "horizontal transition area" I prefer using a brick box myself. With a brick box 2/3 of your barrel should sit on top of your core leaving apx 1/3 hanging off the back, over your new brick box. That box should have an ash cleanout door, should also have a lower ash collection area, and finally that is where your horizontal pipes will start.
Some folks prefer to use a 55 gal barrel to transition , similar to what you were thinking. Only you need 2 barrels . One like you have with removable lid and the bottom removed and another that is cut down to fit around your core leaving the top to be connected to the full size barrel with a second clamp. This method works well as long as it has a large enough exit to not stall the hot gasses.
I assume your mock up is out side. Be prepared that when you put the barrel on your mock up it will effect performance. To truly perform correctly a rmh needs its warm mass to help direct the exhaust thru and up the chimney. Mock up building is for you to test designs and gain confidence with your building skills.
I strongly recommend you get a copy of the builders guide it will help you more than anything!