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Well, most sites, using cURL, for example, can connect to an https connection. And, you'd only have to have the HTTPS setup on your server. The other servers would just have to have support for connecting to yours and that's fairly common.
No matter what you do, there will be some crappy server that someone's on that won't allow your system to work. I've seen servers which simply ban connecting out, for example. GoDaddy, as another example, allows connecting to HTTPS, but through a proxy (their help site shows how using cURL in PHP).
I have a product out which connects to other sites and have very rarely had any problems with people connecting to the other sites to fetch information.
I'm thinking that you're making your requirements unnecessarily restrictive.
Hope that helps. TK appreciated.
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