You sound Great, What Profile and Mic are you using?
In the video I use a small condesor microphone. No need to spend a lot of money.
There are a lot of rigs you can use. Take the rig of an old Twead Amp with a litle gain.
I used the VAB clean 2 from the Kemper Rig Pack 2. I only use the amp and the cabinet part of the rig. I did some equalisation and after that I added slab back and some reverb.
The most important part of the sound however, comes from how you play the harmonica: More or less air, your mouth, your tongue and the cupping with your hands.