Every time I single space h1 & paragraph, the fonts change to match?

Site URL: https://imgur.com/DQjXBAQ

Is there really no way to simply close the gap between h4 (or h1, h2, h3) and paragraph text without the fonts automatically matching?

I assume you're using a Shift-Enter to move to the next line? The problem with doing that is that it's intended as a continuation of the previous line without a full break, so any stylings you have on line 1 will be carried over to line 2. It's also something you should be cautious of using. It's no different than using a <br> tag. You may end up with unwanted results if the screen size changes.

Anyway, more to your question - the best way to close the gap on an element is to reduce it's padding or margins. My guess is that you have a lot of top and bottom padding on your 'p' element (this is pretty common). Or, judging by your image, there is a lot of padding-bottom on your H1. You should be able to adjust this using Custom CSS.

I can't see what your current settings are without a link to your site, but you could do something like this:

h1 { padding-bottom: 2px }

OR

p { 
  padding-top: 2px;
  padding-bottom: 2px;
}

Keep in mind, this will change for all h1 or p elements on your site. I'd have to see your site to determine how to target a specific element.