Um... Luke's father fought in the Clone Wars, but was betrayed and murdered by Vader. Obi-Wan helped Leia's 'father' in the Clone Wars. Luke is only 19 in ANH, so right from the start the Clone Wars were one generation ago. No chance the Clone Wars were really long ago.
Ignoring the prequel films, Luke's father was a "gifted Pilot" when Obi Wan met him first during the Clone Wars. I don't think anything is ever said about about specifically when Darth Vader allegedly betrayed Anakin (ok, it had to happen sometime after Luke's conception), or that it happened during the Clone Wars, just that he was betrayed. We don't know the age of Leia's adopted father, so a young Obi Wan might have helped him 30 or 40 odd years ago. There is nothing saying that Luke was born during the Clone Wars, just that he heard about them when growing up. Also, before the prequels I don't think we got any specific indication of how old Luke and Leia are. I could easily see them aged a few years older without any problem (though to be fair I don't see them as being any older than about 24, Luke especially).
Wait, wait, wait...
ANH... the two references to the clone wars are that Luke's father and Leia's father were involved. Regardless of who those fathers are, the clone wars happened one generation ago.
TESB... Vader is Luke's father, so Vader fought in the Clone Wars, they happened before Luke's birth. Still one generation ago.
ROTJ... Vader is Leia's father, so her father fought in the Clone Wars and her adoptive father was involved in them in some way. Still one generation ago.
The Clone Wars could never have happened "a long time" before ANH. Whether Luke was 19 or 29, the war still occurred one generation previous, and barring a strange situation in which Vader fathered the twins at the age of 60, the wars would always have been placed between 20 and 40 years prior to ANH. Where's the confusion?