Good to know as the Blackbird has been on my list for over a year now. Every time one comes up, something else comes up ahead of it. I was leaning toward the solid base myself, but you just confirmed that this is what I will be looking for.
I understand they retooled this razor after it's first iteration. That 1st one was a terrible design. One razor that made me reconsider using cartridge razors. Instead I just sent the razor back to the makers. I think it was initially released from a Kickstarter project.
I've had both the first version and the current version of the Blackbird.
The first version had very sharp corners at the ends of the top and bottom plate that were clearly felt during the shave.
The second version has rounded corners which makes it feel much more comfortable.