"Trace" as a synonym for "trail" in AmEng
Solution 1:
'trace' does have a meaning similar to 'trail'. It is uncommon - probably the most famous is the Natchez Trace from Nashville to Natchez in Mississippi, set out in the early 1800s.
The implication is that a trail is more 'improved' and used than a trace. If I make a trace and others use it, it becomes a trail. The trace is more akin to the route you took than any kind of improved path.
I would not use the words interchangeably because of the rarity and this difference in meaning.
Solution 2:
I grew up in Montana and "trace" is commonly understood here (and as I understand it in other mountainous areas of the US) to mean a newly cut trail unsuitable for vehicle travel of any kind. The terrain and/or vegetation prevent travel except by foot (or sometimes horse).