I don't know what the answer was in the original case, but if you have similar issue, where you see set-cookie SMSESSION = *** , but the SMSESSION is not sent back to site on subsequent requests. Then there is somethign about (or wrong) with the set-cookie command, and it did not take.
There can be a bunch of reasons : some are :
a) /secure and sending back to http site,
b1) wrong domain domain set to = .x.x and request from domian=.y.y,
b2) domain missing leading ".", or missing domain, means is host only cookie, so not sent to other host in domain.
b3) Chome rejects set-cookie from some .amazon.com subdomains (compute or something like that)
And more.
So best to look carefully at the Set-Cookie rquest you got back, and also check the F12 console for errors.
Post fiddler/ .har trace here is you want and can check it.
Cheers - Mark