Where to find Omega Seamaster 600 135.011 replacement leather straps?

Hi Roger,
Do use the original buckle! It is a part of the history and originality.

As for straps there seems to be a common opinion that it is not vital that they are Omega.
Personally I would save the original strap for the sake of history, and then find a OEM I like to wear.
Omega never actually made the straps. They came (with the Omega print) from independent suppliers.
There are TONS of suppliers.

Measure the buckle inner width and the width between the lugs.
Let's say they are 16 (buckle) and 18 mm (watch lug).

Then consider if you have a normal wrist or need something longer or shorter.
Personally I have a 19cm / 7.5+inch wrist and the "normal" length straps work well.

Depending where you are, find a good supplier to keep shipment cost down.
Here is one German example: http://www.watch-band-center.com/shop-watchstrap.html
I do not say they are better than others, but they do stock several quality brands of straps.

Very often you will find a tang/buckle is already attached to the strap. This can be easily swapped with your original one.

Good luck!

PS! You can also check eBay. Tons, and tons of straps, also Omega badged ones.

9mm(!)? That is indeed unusual for a mens strap.
I think it is safe to say that strap was never intended for that watch!
Where are you located? Europe/US?
I checked on eBay, and most listings for straps with "Omega" buckles seem to have at least fake buckles. They just don't look right.
Compare this one (which I think looks ok);
http://www.ebay.co.uk/itm/Omega-Vin...el-strap-band-buckle-16mm-N-O-S-/391248526090
With this one (which I think looks like the hard labor of Chinese child hands):
http://www.ebay.co.uk/itm/VINTAGE-1...TRAP-BUCKLE-/221848715519?hash=item33a736c0ff

The strap you should look for IMO is a 18/16 strap.