You are not at all mistaken. All Eagle Squadrons started with Hurricanes and finished with Spitfires. Actually there is no little confusion on all this. There were three Eagle Squadrons, all becoming operational well after the Battle of Britain. Several Americans did fly with the RAF during the BoB but they were scattered across several squadrons, some flying Spitfires and others Hurricanes.
The first Eagle Squadron (No 71) with the marking XR, became operational with Hurricanes on 5 February 1941. It transitioned to Spitfires in August and was stationed at Martlesham Heath. The next was No 121 with the marking AV, formed at Kirton-in-Lindsey on 14 My 1941 and also equipped with Hurricanes. No 133 Squadron (markings MD)was reformed as the third 'Eagle' squadron in the RAF on 1 August 1941 at Coltishall and initially equipped with Hurricanes and transitioned to Spitfires in October. So it is fair to say that all of the Eagle Squadrons started with Hurricanes but spent most of their combat time in Spitfires.
While the Eagle Squadrons missed the Battle of Britain they were very effective. Through September 1942, the squadrons claimed to have destroyed 73½ German planes while 77 American and 5 British members were killed. 71 Squadron claimed 41 kills, 121 Squadron 18 kills, and 133 squadron 14½ kills. All three squadrons operated together only once at Dieppe.
In September 1942 the three squadrons were officially turned over by the RAF to the USAAF to become the 4th Fighter Group. They flew out of England and later North Africa with Spitfire Mark VBs and for some eventually Mark IXs until finally converting to American fighters in late 1943 to early 1944.
Also, if you want to depict a flight of aircraft the only marking you need to change is the last of the three letters. The first two are the squadron identifiers, as in "XF", the last one (or two) are for the individual aircraft. Squadron commanders frequently flew in the "A" aircraft, with other letters descending according to rank but that was far from universally honored and often jumbled due to operational priorities.
