Do exactly what you did. Yes, the external willl be dog slow depending on type (SSD vs spinning) and interface (Thunderbolt, usb 3, or usb 2). Once booted run Disk Utility if needed to format the internal drive, then run CCC to clone the external to the internal. When done, shut down and boot from the internal drive. This is exactly what I did when upgrading my MBA internal SSD. I had an external thunderbolt SSD so it went fairly fast.