Use JUCE as much as you like, but please, stay away from those 'out-of-the-box' horizontal sliders it seems to prioritize (given how they swarm in the many VSTs made with JUCE).

If sliders are vertical in the real world, there’s a reason for it that Bruce “Tog” Tognazzini summarizes perfectly:

“Most of us […] have our forarms mounted on a pivot we like to call our elbow. That means that moving our hand describes an arc, rather than a straight line. Demanding that pivoted people move a mouse pointer along in a straight line horizontally is just wrong.”

Source: https://www.asktog.com/columns/022DesignedToGiveFitts.html

JUCE' GUI framework is extremely versatile - if that default irks you, its a couple lines of code to get pretty much any control to behave itself.

DJs routinely change the playback speed to match tempos.

It’s easier if a track’s tempo stays the same throughout its duration, but even if it changes, DJs will adjust the playback speed on the fly.

As far as syncing is concerned, the actual value of the tempos doesn't matter at all.

"Harder, Better, Faster, Stronger" was built around a one- or two-bar loop sampled from Edwin Birdsong's "Cola Bottle Baby."

Daft Punk determined that this loop had a tempo of 116.527 BPM and played it a semitone higher.

116,527 * 2 ^ (1 / 12) = 123,456 BPM