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What you want doesn't exist so far as I know. Probably not much of a market for this either. About 10 years ago now, there was a spate of LS conversions and some suppliers tried to market sets, most of which didn't work. Look through GordonM's posts on the subject here in the C3 forum. He's sold his C3 and doesn't post here, but back then went through a long expensive search for ordinary, not side pipe headers. If you have deep pockets, American Racing Headers could build you a custom set.
On my 71 C3 LS swap I used Patriot mid length headers for 55-57 Chev swaps. I had to mod the right side a bit to make them fit. Seems to me if the mid-length works for you it would be easy to match them up to side pipes.
No photos of it installed, but those bends look like they align with the typical slanted LS manifolds. They might even work with the LS7 takeoff manifolds that some folks use.
OP, if you just want 69 C3-style side pipes, the stock LS6 manifolds might also work. Weird oval opening, but they exit similar to the stock C3 manifolds. I have not test the fit of these, though I do have a pair. Also, manifolds, not headers.
There was a discussion on these headers at one time. Different pictures than the web site shows and I considered these for a while but decided that the z-bar went right through the middle. Some more research suggest that the cast iron exhaust manifold on my LS3 flowed pretty well and there may have even been some published data on that that I've since lost. Overall the cool factor for headers was lost for me at that point. Thanks Joe for the reminder and hope this helps somebody else with undercar decisions.
As to the outside exhaust, the original cars with 427's had a single exhaust tube to the side. Unless one is looking for the bundle of snakes aftermarket sidepipe, seems like the factory cars weren't all that stifled. Any good exhaust shop ought to be able to mate an LS manifold to the outside exhaust.
If you're ok with a single pipe instead of the headers extending outside the body, 98-02 F-Body manifolds/shortys will fit (98-00 have EGR port, 01-02 do not). Then you can just run the single pipe outboard from there.
They're not side pipe headers but search Speed Engineering 25-1026-1 for a long tube option. They're not listed as being for a C3 corvette but they fit. They just need some minor massaging around the collector and the #3 cylinder spark plug. They are the closest you'll find out there for under $1,000 and they're stainless.
My engine in this picture is in the "rear" mounting position for LS swaps. A buddy let me borrow the headers to test fit. My actual exhaust is on the ground and uses BBK shorty headers for an 01-02 F-Body. You can kind of picture where they would end based on the flanges.
I love this forum but hate that so many just follow. $300! These headers fit perfectly especially if you are using R&P steering. If you are using a borg box you need to dimple #5 a little. Stock box should be no issue. Using these in both my 69s one with BHP motor mounts other with sbc/lsx adapter plates. Work with Vette and F-body oil pans, I can confirm I've ran them both in my cars. Flange is steel the pipes are stainless.
Ground clearance is great no issues there either and they point out straight no off angle using F-body LS motor headers. Weld a v-band to them and off you go!
Sorry I missed the side pipe part at first the simple answer is No! Not enough volume to make it in mass to = cheap.