Are 340’s rare

Be careful what you wish for. The 408 may not be what you think you want. I have a friend with a 396 camaro and a 408 dart. Both engines are very similarly prepped and geared. Now he raced his cars numerous times against each other and said the Dart always beats

the Camaro off the line but by 80 mph the 396 passes and walks away from the over square 408 Dart.The 396 with 3.75 stroke just flat out revs quicker. The 408 certainly makes more torque if that's what you want and may be better suited to a heavy vehicle. The Dart had 3.23 and the Camaro had 3.31 gears.
If it's a big port 396, it's probably got 30-40% more head flow than your typical 408 head. Even a stock oval port bbc head will flow 50 cfm more than a stock 440 head. The peanut port bbc that all the chevy guys laugh at outflows a 440 head. Flow restricted 408s make great torque, great for driving around with an auto and mild gear. To run with a bbc, a 408 will need a BUNCH of good heads and headwork. (Talking basic street car, not racecars, John C, lol)
Edit: how do you KNOW its a 396/402? I tell everybody mine is "a hundred over 396". It's not my fault if they think 421, instead of 496. Sixty over 427s rev even better than 396s!