The user "uncon" on the #Citrix IRC channel on FreeNode gave me a solution that does exactly what I want: Use the Citrix Receiver Chrome Extension. It lets me log in to my company's storefront and loads ICA files directly, creating my "full screen" 1920x1056 window with no mouse offset. PERFECT!
https://chrome.google.com/webstore/detail/citrix-receiver/haiffjcadagjlijoggckpgfnoeiflnem/