Re: Santoni IIRC their straps are only available on the 8-day hand-wounds, so the croc straps on mine probably aren't from them.
As for the Gladstone - I wholeheartedly agree; unfortunately it's not mine, and I can't seem to find anything quite like it. I've half a mind to just commission one similar to it for myself.
You can get/order a Santoni strap from IWC.
The strap is stupid expensive tho, around $500-600 bucks.
My ex-gf's steel and gold Connie was a few years earlier and differed in that the bezels on the earlier models were flat. From the photo it looks like yours was the next generation which had domed bezels. Again, nice choice share some more photos when you have time.