1965 Barracuda with a 360...intake suggestions?

John;

Do a serach or post the question of intake manifold clearance if it doesn't get answered in this post. You will NOT find fitment issues or words saying it's a go for your or any car at the manufacures web sites.

What you will find is height measurements and how they do it. Edelbrock has a diagram you can view on how to measure.
Use there method to measure your current intake. Do the math, find the difference. Put clay ontop of the current air cleaner and close the hood. Meausre the clays height. Do the math. It fits or not at this point via the work I described.

I don't know what the gear ratio is (I know I just lost credibility on that last statement...).
Thats OK and no, you did not loose anyting. Most people do not know. May I sugest that you take the time and change the gear oil in the rear. (Mantainace) While you have the cover down and both wheels in the air, rotate the tire and watch the inner gears spin around. Look at the ring gear closely. Stamped into the ring gear is the ratio.

If you can take a picture of the rear, we can I.D. it. It may be a small 7-1/4 which should be sold to the scrap metal yard and the cash rolled over to a 8-1/4 or 8-3/4. The 8-1/4 is cheaper and more plentyful. The draw back is strength, though it'll be tuff enuff for 400+ HP. 8-3/4 cost $$$$$ Though I like the center section drop out abilty for reasonably quick gear ratio changes.
Your call.
There more likely to be a big bolt pattern wheel on the 8-1/4, early 8-3/4 have the small bolt pattern.

IMO, A decent street car without getting headers on the 360 could look something like this;

A K&N on top of a 650 carb of your choice on a RPM or equal intake with a cam to comploment the desired rear ratio. I like 3.55 for a driver with brass ones. While the heads remain stock, a cam like a Comp XE 262 or equal in a 9.0-1 compression ratioed engine would be a real nice and powerful driver.

If you could or wanted to slip in headers (There a thread going on about it here on the Mopar Muscle article that makes use of tti's new headers for your smaller engine bay A body)
That would be great and open up some power restrictive bottle necks. I, myself would step up to the next cam (XE268 ) and pocket port the heads with stock back cut valves. Or out of the box Edelbrock heads.
Call it a day.

The stock Carter you have can work great. The OE 4bbl. intakes are good in there design. So do not shy away from one if hood fitment, cutting a hole in the hood or money is an issue. (An AVS carb needs the flat plats over the rods so you can use the Edelbrock rod kit. The Edelbrock rods are AFB designed, which mean there a 2 step rod, not a 3 step rod like the AVS's.)