Would any of the Harmony (ideally either the 880 or 1000) be able to be programmed so that it sends a signal xx seconds apart?

I have a motorized projector screen, which does not have limit setting. Hence, it refuses to stop at a preferred length. I am hoping on a workaround by using a Harmony 880 to send "DOWN" signal, wait 30 seconds, then send "STOP" signal.

can't speak for the 880, but I have a 1,000. i can set a delay of up to 25 seconds between key presses. However it will do up to 60 seconds delay after power on. Sooo, you can map the down control to power on, then the stop control to another button.

As mentioned by Jabo75, you can adjust the device delays (under Device > Settings > Adjust the delays). The limit is 60 sec (60000 ms) for the Power On delay, and 25 sec (25000 ms) for the other delays like the Inter-Key and Inter-Device delays. You could use the activity sequence feature to map the Down Stop sequence to a key but you can NOT add a delay in between. I believe it will invoke Inter-Device delay. As a precaution , I would set both the Inter-Key and Inter-Device delays to the same large value. You could also insert a "dummy" (do nothing) command in between the Down Stop commands to get 2 delays.

The preferred method is to add the sequence, including delays, using the activity start/leave custom actions (start/exit macros). Review the activity and select the option "Yes, but I want to add more control of options and devices for this Activity", then click next/save a few times until you get to the custom actions configuration page. The custom actions allow adding delays between commands. The limit is 10 sec per delay but you can add consecutive delays to get the desired value.

This is doable, you just need to call harmony support and speak to someone at their level 2 support. Not all of the people there will be willing to assist you but this is doable, all they need to do is modify the setup of your device. Make a custom power on sequence, for example; send power command, then delay for X seconds, then STOP command. It has to be done manually from their end not yours. However, you can also try other suggestions mentioned by jlet and be able to get it working with a bit of fiddling.