Does this sound like a reasonable way to go about this? I just don't want to post the story prematurely and not have it make sense.
Yes, the way you're doing things is fine. That's the way I'm currently handling my third-person omniscient story. One character focuses more on his thoughts being a leader, calling back on experiences that no other character has. Another thinks more analytically, looking at everything as if it's data or machines. Another just bounces around from one thought to the other.
If you're worried about being consistent, you can read back over what you wrote and check for proper characterization. If a character says or thinks something that doesn't sound right, you can catch it before you reveal the chapter to readers. Either being careful during each scene or editing after writing is you best bet to making sure everything is right.
The one thing I'm unsure of is the numbering. It sounds a little too much like the looked-down-upon POV labels that fanfic writers use, where they have "
Character A's POV" before each scene. It might be different in your story, though. Still, if you're concerned about making sure the reader knows whose POV we're switching over to, use their name in the narration or have a thought that is distinctly theirs.
Since you posted after dudebot and I didn't know about it, I wrote up some other advice that you may or may not need. I'll leave it here for you in case.
Just don't abruptly change the point-of-view in the middle of a scene. If you do need to change narrators in the same chapter, ease the reader into it. Either use the advice I've seen of using a scene separator, which could be a centered line or three asterisks in a row, or by having the character that you're switching to do something to gain the reader's attention.
When writing from different point-of-views, keep in mind what a character might sense, notice, or think about based on who they are and what their experiences are. If one character has a distinct way of thinking about something compared to other characters, then you'll write about that and it'll come through to your readers.
You should be writing in the point-of-view of the character most important to the scene. Whose thoughts and feelings should the reader be focusing on during this time? Ask yourself what the advantages are of writing in one character's viewpoint compared to another.
And there will be times when you're way more comfortable writing in some character's viewpoints compared to other characters. It happens. Just keep trying, write through the scene in the difficult viewpoint, and then you can go back and add anything that should be added.