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I find that having the words memorized really helps, then you can focus on your playing. Seeing helps, too.

Might be a bit late, but here are my 2 cents:

I read that the left hand notes are C-G-F-C. I presume you are using 5-1-5-1 fingering? so the jump would be between G and F. The important note here is G (not to mean accent it) for the preparation to jump to F. Very common people would focus the landing (target) than the take off.

1st finger resting on G, play G with a feeling of "bouncing" as soon as you hit it (like it has a spring underneath the thumb). Your forearm should be lifting up as a result of the bounce. Then drop back to the note G without any effort and let gravity do the job.

Once you are familiar with the bouncing feeling, play G then bounce to F and rest your 5th finger there without playing. Make this movement as fast as you can between the 2 notes. Practice until you can bounce and land accurately on F (still without playing F). Once you feel that you've got it, play as normal. When you play at normal tempo, make those movements as small and as economical, so small you can hardly see it but you can feel it.

Good luck!

Oh, sorry, I didn't describe in enough detail what I'm doing.

It is common in some styles of church music to play a left hand pattern on simple chords, usually I, IV, and V, where you first play the root in octaves, followed by the chord up an octave. So for example you would play C2 and C3 with 5 and 1 of left hand as a chord with pedal, followed by C3 E3 G3 as a chord on the next beat. Then the chord change may follow. Usually the right hand is tinkling along on the melody. That requires a shift of the left hand, but it's not a difficult shift because you have a finger on C3 so you know where it is without looking.

What I'm doing is based on this. I play C2 C3 together 5 and 1 of left hand on beat one, and while holding I play C5 E5 G5 with the right hand on beats two and three. I don't want to play the melody here, I'm staying out of the way of the voices.

Then I need to change the chord, and here's where the leap comes. I need to move the C2 C3 left hand to play G2 G3. I play the root note of the chord in octaves with the left hand, followed by the entire chord in the right hand a couple of octaves above it.

It's a method of adding variety to a simple accompaniment, and at my skill level I stick to simple if I'm playing in public.

Well, it's done.

The performance went well.

And I cheated big time. I recruited extra singers to take that pressure off me. I memorized the piano part, and refrained from singing except where they really needed it. So I was able to look at my hands as needed, and got through it fine.

I still need to keep working on leaps, but this one worked out.