By way of an update: I've upgraded VirtualBox to 6.0.10.
In an attempt to isolate some variables, I switched to a non-minimal precise64 base box, then added the following statement to the hashicorp/precise64 Vagrantfile:
config.vm.network "private_network", ip: "192.168.56.100"
Somehow, this prevented the "VERR_INTNET_FLT_IF_NOT_FOUND" VBoxManage error mentioned in my original post, allowing VM to boot. The provisioning successfully SSH'd into the running VM to update the system via apt and install the VirtualBox 6 guest additions. Adding the statement:
config.vm.network "forwarded_port", guest: 22, host: 2020
also suppressed the error.
Bolstered by my success, I tried to provision some CentOS 6.10 & 7.6 VMs (based on bento/centos-6 and bento/centos-7, respectively). The VMs provisioned from these base boxes returned the same "VERR_INTNET_FLT_IF_NOT_FOUND" VBoxManage error until the config.vm.network properties were set.
Perhaps an incompatibility between Vagrant v2.2.5 and VirtualBox 6.0.x?