After a lot of dumps and screenshots Citrix Support narrowed the issue down to the CitrixvirtualSmartcardCsp.dll, which is a new Smart Card feature added to the VDA after version 7.6.
In Process Explorer, right click the application that is consuming the CPU and click properties. Under Threads, select the thread that is consuming the CPU and click stack to view the running DLLs.
As long as you're not using the Smart Card feature, it can be disabled to allow InfoPath to function properly.
Change the Type key to 0 under HKLM\SOFTWARE\Microsoft\
Cryptography\Defaults\ Provider\ CitrixVirtualSmartcardCsp
A reboot is not needed. This will take effect immediately.