brundlefly
2:43 AM, it appears you're overclocking your CPU. I'm not sure if that (or some setting related to it) could cause this, but I wouldn't rule it out given how unusual the problem is. How hard would it be for you to reconfigure for rated speed?
You're right! I am indeed overclocking with much stability. Swapping back to default CPU/System parameters is relatively easy, so I went ahead and did just that and proceeded with the test. The result is the same: big delay in the recorded audio.
This is some seriously funky stuff going on here; impossible to narrow down. The "issue", even if it wasn't a true bug, was gone in X2a but only later in the game. I submitted a bug report of this very thing for X2a! Little did I know that Cakewalk would never release an X2b. But then the issue seemed to go away by itself. I reported in this thread that X2a worked well; no issues. However, now in X3e, the issue seems is back! So now it's worthy of me to try to figure out what setting change--what tweak--I did in X2a that cured the problem.
This is the best thread of yesteryear that I could find on the exact same issue. The issue has been around since 2011 and maybe earlier (I think some threads reporting count-in problems date back to 2008). See
http://forum.cakewalk.com/tm.aspx?m=2413605&p=3. Brundlefly's been helping with this topic since at least 2011! Thanks for sticking with it!

Unfortunately, for all users, no complete resolutions nor the identification of the problem have been mentioned since then.