That's great! Your are absolutely correct, most sites seem to originate in pre-2000.

Just two additional ideas:

For the problem you specified I did find a interface which gives you a day view of both destinations with the corresponding times on both sides, and colored backgrounds (green for good meeting times, yellow for too early or too late or midday and red for night) so that you can easily find out an optimal meeting time (I guess it was possible to add more timezones to it), however I cannot remember the site.

For the interface you created I guess it would be nice to add an analog clock over the input, which can be changed via dragging the hands to the specified time and the other clock updates it's time in real-time.