Awesome, that one simple line of CSS worked! I think I had tried that on the iframe itself, but apparently not on the svg element. I appreciate the help!
The SVG specifications state that all SVG elements that create viewports should have overflow: hidden in the browser's default stylesheet. However, browsers disagree over whether this should include the padding area or not: if you follow the description in the SVG specs, as Firefox does, padding would not be included. However, general CSS/HTML layout does not consider content in the padding to be overflow, so Webkit/Blink/IE browsers do not clip it with overflow:hidden.