I Understand that is what EA requires but to send this information would be breaking Steam TOS and a inadvisable risk as per valve support.
You need to discuss this swtor or steam support , a public forum is not going to resolve this for you
all i can provide you is you need to provide the screenshots as detailed for swtor to provide the gametime, steam have had over a year to say to swtor they have had an issue with the requested screenshots and to date have not said a word
I have this is where Both SWTOR Support and Steam support have sent me.
No one at EA seems to care or be able to do ANYTHING there is no path for escalation from any source to find a resolution with any form of customer support.
EA has setup all of their customer service to deal with only the lowest level of issues and nothing more.
As for Steam, No reasonable and intelligent person would think there is any expectation for valve to be aware of a internal tech/payment processing issue glitch/hiccup on EA's side.....
Nor is it reasonable to expect that they are aware that SWTOR support is asking people for screenshots and just because I may be the first person to notice or care what is being asked of us potentially could put us the customers at risk.
Please remember this is information that valve implicitly states not to share to others so logically one can assume that just because they aren't aware of EA's solution to this issue doesn't mean they wouldn't have issue with something they implicitly state not to do.
ALSO the steam receipt provides all relevant information needed and is a readily available proof of purchase provided by Valve so we can safely assume that's what they expect me to use to as proof of purchase or why would they provide it in the first place?....
You can call swtor support when the line are open , this is the main method of customer service for those with an account issue with their swtor account
