There are various other options you might try, beyond what's been suggested already. Perhaps the most comprehensive guide to mapping cave systems for CC3+ is in the very early Annual Caves & Caverns modern style, as the mapping guide for it demonstrates how to use a top-down drawing to create a workable cross-section as well. That mapping guide also has a link to the UIS Working Group's website, which has a PDF of various real-world caving symbols, including for illustrating heights, that can be used that way, and a further website that has detailed example maps as further inspiration.

For more "art-style" dungeon drawings, where there's overlap between features on different levels, the classic method is to use a dashed line to indicate the underlying part - as I've done recently for the Nidag Temple map, for instance.

I used these, with a mixture of other tricks (shaded stairways, shadow from an angled ledge, different floor fill styles/colours) on the Rosebud Caverns map from the Atlas last year as well, which may give you a few more ideas.

Even with a "flat" dungeon level, it need not be the same level everywhere; early versions of D&D encouraged use of sloping passageways and similar features for example, based on real-world caves and artificial underground places, although that often simply made for player headaches in trying to map things during games, so tended to disappear from practical gaming use very often.

Don't forget too that something as simple as an arrowed line can help show where a gradual slope is, drawn on or beside an affected area, and different styles of arrow can be used to show different degrees of steepness.