Need a small piece of Teak
Assuming your tiller is straight (or you don''t want to recreate the existing curve), and your 1" dimension is the actual rather than nominal thickness, then a two-piece lamination of store-bought 1/2" material would be ideal. Finding 5/4 (what a retailer calls net 1" thickness) boards only 3'' long is likely to be tough, unless you actually do find someone with scraps.
In Santa Ana (30min. S. of LA) there''s Austin Hardwoods which has a decent supply of misc. hardwoods milled to 1/2" thickness. There may be others closer to you, like maybe Saroyan, I''m not sure.
If you decide to laminate teak, use either resorcinol and lots of clamps, or one of the polyurethane glues (Gorilla Glue...), and wipe the surfaces with acetone before gluing, to remove surface oils. Still use plenty of clamps with the Gorilla Glue, but not as many as are needed for the resorcinol.
Lastly, most tillers are mahogany, which accepts finish better than teak and is stronger for its weight, as well as being easier to laminate.