Moving my VPS from VMware to Fuga was successful. First I copied the VMDK from the ESXi host to a Fuga instance with enough storage:

scp some.esxi.host:/vmfs/volumes/storage-node/autostatic1.autostatic.cyso.net/autostatic1.autostatic.cyso.net-flat.vmdk ./

And then converted it to QCOW2 with qemu-img:

qemu-img convert -O qcow2 autostatic1.autostatic.cyso.net-flat.vmdk autostatic1.autostatic.cyso.net.qcow2

Next step was mounting it with guestmount:

guestmount -a /var/www/html/images/autostatic1.autostatic.cyso.net.qcow2 -m /dev/sda8 /mnt/tmp/

And changing some settings, i.e. network and resolvconf. When that was done I unmounted the image:

guestunmount /mnt/tmp

And uploaded it to my Fuga tenant:

openstack image create --disk-format qcow2 --container-format bare --file /path/to/images/autostatic1.autostatic.cyso.net.qcow2 --private autostatic1.autostatic.cyso.net.qcow2

Last step was launching an OpenStack image from this image, I used Ansible for this:

- name: Launch OpenStack instance
  hosts: localhost
  connection: local
  gather_facts: no
  vars:
    os_flavor: c1.large
    os_network: int1
    os_image: 5b878fee-7071-4e9c-9d1b-f7b129ba0644
    os_hostname: autostatic1.autostatic.cyso.net
    os_portname: int-port200
    os_fixed_ip: 10.10.10.200
    os_floating_ip: 185.54.112.200

  tasks:
    - name: Create port
      os_port:
        network: "{{ os_network }}"
        fixed_ips:
          - ip_address: "{{ os_fixed_ip }}"
        name: "{{ os_portname }}"

    - name: Launch instance
      os_server:
        state: present
        name: "{{ os_hostname }}"
        timeout: 200
        flavor: "{{ os_flavor }}"
        nics:
          - port-name: "{{ os_portname }}"
        security_groups: "{{ os_hostname }}"
        floating_ips: "{{ os_floating_ip }}"
        image: "{{ os_image }}"
        meta:
          hostname: "{{ os_hostname }}"

And a few minutes later I had a working VPS again. While converting and uploading I made the necessary DNS changes and by the time my VPS was running happily on Fuga all DNS entries pointed to the new IP address.