A tip that works with singing-in-tune-with-synth-settings comes from a vocal intonation study by Ternstrom and Sundberg. They give this piece of advice for practicing harmonic tuning.
When working on getting the harmonies in tune, you need to sing without vibrato. You can use vibrato during performances, but always practice harmonic intonation without vibrato.
Vibrato obscures beating. Beating is the “wah-wah-wah” sound between two or more simultaneously sounding notes. Beating creates a cue that singers use to tune-up chords. Obscure the beating with vibrato, and the harmonies become less accurate.
Similarly, Charles Shackford advises that you should take your time tuning up harmonies. The longer a harmony is held, the more in-tune it becomes. Joe Wolf says that taking enough time to accurately tune allows the waveform sufficient time to develop.
Therefore, when using the keyboard as a harmonic sound model, you should pick a synth sound that has a sustained tone. Furthermore, it needs to have as little vibrato as possible.
It may not be possible to find keyboard programs without any vibrato, just pick the best option. (The audio example below has some vibrato.)
Notice that the example below has long rhythmic note values at a slow tempo.