I agree with the metronome and going slowly!

First, go as slow as you need to. Determine how fast you can cleanly change between two chords. 20 times a minute? 30 times? Set a metronome to that. Right now, you're not playing to the metronome. The metronome is playing to you. Practice this until you're really comfortable at this pace.

Eventually, bump the metronome up slightly. If you are comfortable with one change every two seconds (30 bpm), bump it up to 35. Work at this level until you can cleanly switch between two chords at this slightly accelerated pace. Take your time and drop back back to a slower level if you need to.

Rinse and repeat. It takes time. Two mantras:

1. Slow is smooth and smooth is fast.

2. Perfect practice makes perfect.

If you play slowly but accurately and cleanly, you'll develop excellent technique. And excellent technique yields speed.

And don't practice so fast that you're sloppy. You're building muscle memory. Every time you change chords, you're training your nerves and muscles. If you train them sloppily, you'll play sloppily. And if you train them cleanly, you'll play cleanly.

Lastly, know when to quit. Your body actually needs you to stop and give it 24 hours to build the nerve connections to play what it's learned. Practice some, stop, and come back to it tomorrow.