First off. Never trust youtube videos, often idiots upload videos and the frequencies aren't even correct, or excessively clipped.
I'd just use REW or Audacity tone generator, Audacity has a fade in/out feature. Adobe Audition if you want to control the slopes yourself (but not free).
You could install the cones inverted with the magnets hanging out and use a laser thermometer from walmart/any hardware store. If the coil is too hot to touch, then that is starting to approach the heat danger-zone.
As for bottoming, you'll know because you will hear clacking and the cone excursion will be crazy (the UM-18 is rated for about ~2inches P-P, 1inch inward and 1inch outward).
Once you get to know the system better then you can mount the drivers normally.
Ported boxes require a HPF at the tuning frequency otherwise it will bottom out below that, but since this is an exhibit you'll have known material so it is not really required, as long as you are careful.
For starters I'd set the limiter to 300w @ 4-ohm for 1 or 600w @ 8-ohm for 2. It "should" be able to do that wattage all day long. You'll have to perform long-duration tests to confirm, ramping up the wattage slowly until you find the thermal limit.
An 8 hour exhibit will be more stressful than a 3 minute song.
You'll want to keep an eye of the amplifiers too to make sure they aren't overheating.
That is what 30 day and 1 year warranties are for, costco-style I suppose!