Joining plywood or hardwood for long countertop

[johnny means]

First join the boards like your Momma's life depended on it. Doesn't matter how as long as you know they will absolutely never move in relation to each other. Next take a grinder or an aggresive sander like a Rotex and grind a 1/4" trough down the seam. Go about 3" wide on either side. You want the sides to slope as gently as possible. Fill the void with Bondo, filling slightly above the surface. Sand flush with a block sander that spans the void. This works particularly well with MDF or maple ply as they paint up to a smooth finish. Personally, i reserve this level of hardship for top end commercial exhibits with huge budgets, kids playrooms get a glueline.

[Gene Takae]

I suggest using MDO. Waterproof and excellent for painting but will need to order from a plywood supplier

[Mike Cutler]

First join the boards like your Momma's life depended on it. Doesn't matter how as long as you know they will absolutely never move in relation to each other. Next take a grinder or an aggresive sander like a Rotex and grind a 1/4" trough down the seam. Go about 3" wide on either side. You want the sides to slope as gently as possible. Fill the void with Bondo, filling slightly above the surface. Sand flush with a block sander that spans the void. This works particularly well with MDF or maple ply as they paint up to a smooth finish. Personally, i reserve this level of hardship for top end commercial exhibits with huge budgets, kids playrooms get a glueline.

This is the way I would do it also. Although I might not feather it in as much for a kids playroom counter top. Good practice though.
If you have a router, buy a finger joint bit to make the edge joints. Slam them together, and you have more than enough glue surface area.
Of course, you can always use the project as an opportunity to invest in a Domino if you'd like.,

[Al Launier]

The question I have, considering the difficulty in getting whatever material you want for such a long counter top, is do you really need to make it 13' long? If you could design it for a 12' length that would solve your seam problem as there are a host of materials obtainable in 12' lengths. Without knowing of your design intent, would shortening it 6" on either end, or simply an open section in the center be acceptable?
It seems like this is an example of where one should design around available materials rather than the other way around.