There is a solution to what you seek (I'm sure there is more than one). My answer requires two non-conventional approaches to what we call a 'secure connection' and how you receive the 'client code'.
You need a physically pre-shared key that initiates a secure connection, and because it's pre-shared it doesn't have to be RSA, which then opens up speed opportunities and higher levels of encryption security for you.
Physically pre-share your client code in a similar manner, i.e., download the code from a cd in a magazine or from a pre-paid card sold in a market. This stops the MITM from sending you tampered and exploited clients, which ssl allows. Once client is known to be secure, and a real secure connection, mentioned in (1), is established, the client code can be updated.
With the combination of a pre-shared key that develops a secure connection and client code that can pass a checksum, you can achieve what you are after.
Ideally, we should have pre-shared secure connection keys available in the market now, but we don't. So, for you to do it alone, would require to implement something similar for you website specifically until people in this country get their act together with some real security. You would have to give them keys over your phone, through the mail, etc. And your client code would most likely have to be a browser extension to install it due to cross domain security issues.