Schubert's Landlers and German Dances.
Middle movements of piano sonatas from Haydn or Mozart.
Also, just peruse a traditional songbook or hymnal, there will be 3/4 songs like Happy Birthday, The Star Spangled Banner, or God Save the King.
...debates between different people about whether the piece in question was really in 3/4 time or 6/8 time
That would be a debate between people who don't know the difference between simple meter 3/4 and compound meter 6/8, 3/4 has three strong pulses, three beats, but 6/8 has two. Those two meters are distinctively different.
However, the difference between 3/4, 3/2 and 3/8 is more subtle. All have 3 beats, but historically each meter was used for a different characteristic feel. The essential idea is during the Baroque period meters with smaller bottom numbers were played in slower tempos. You can group them together as simple, triple meters.
If triple meter is what you want, and not specifically just 3/4, you could also look at the dance called the sarabande which is in 3/2 or the courtante which is sometimes in 3/2, sometimes in 3/4. Both dances were common movements in the Baroque dance suite.
...I'm struggling to write stuff that doesn't sound blatantly like a waltz.
This may also have to do with "waltz style" accompaniment which is the "bass, chord, chord" pattern. You can try to escape that two ways:
- write a melodic bass, minuet and courtante dances will provide examples
- try a non-waltz tempo
Some Romantic era dances like the mazurka or lander may sound waltz-like, because they often use the bass, chord, chord pattern. If you want to avoid that, definitely look to Baroque dance examples.