Was there ever a fuel-injected Spitfire?
Yes there was. A Spitfire which was converted by Daimler Benz engineers to use a DB 605 engine. See the following links:

https://www.klassiker-der-luftfahrt.de/geschichte/flugzeuge/daimler-benz-versuch-die-daimler-spitfire-die-db-spitfire-zeigt-gute-flugeigenschaften/615458?seite=2

https://defenceoftherealm.wordpress.com/2014/11/17/the-franken-spitfire/