If it's only the day (and not time of day), then securing the next ten years would only take around ~3650 trials. Doesn't seem too bad.
(And the can't make it too precise, if they want their attack to work even if you don't use the tool at exactly the right microsecond.)
Yeah, at a glance doesn't seem too bad, would depend on how fast you can actually do one prefill+full decode run. Say you do it with 10 seconds per iteration/test, then it's only ~10 hours to verify next ten years. Definitely doable.