The short answer is I don't know of a perfect way to do this. If you know of visualizations done in Tableau that meet your criteria, I would be interested in seeing a link to figure out what they did. That being said, if I was trying to accomplish something similar, these would be my approaches.
1. The best option would be to find a WMS server that has exactly the land area you're looking for.
2. Washing out your map completely is a viable option if you're leveraging a filled map with enough land area covered.
3. Turning off country names/land cover/whatever else you'd like and leaving the map leaves the background as a pretty innocuous intrusion into whatever you're showing.
4. Dual axis a map (may have to be blended but hopefully you have datapoints from all 50 states in your data. Use 1 axis as a filled map at the state/country granularity and wash out the map completely. This will leave a filled background of the US, though you lose the land cover/roads/names you may have originally wanted. Dual axis this map with your actual datapoints. The downside is if you are leveraging quick filters and filter out a region/state that background would go blank, though that might actually be a nice feature.
5. If you're only showing things at a high level and wouldn't have to custom geocode many things, you could actually leverage a custom background image and just place the points on the map via manually entered x,y coordinates. This gets exponentially more difficult if you need filled shapes as you will need to leverage custom polygons.
I'm still unclear how to make this happen. I am using a dual axis map with the base map being a filled map and the second map being circles plotted on the base (U.S. map). If I washout the map it makes everything white and all I can see is the outline of the state where I have data. That won't work for me
I wish there was a way to just check remove Canada and Mexico from view
Unfortunately that is the only way I know of accomplishing this. Have you tried the suggestions from Ben? Also you might want to check the Ideas to see if this exists and if not create the idea yourself