Of course, by all means, do what works. No band member is going to come up to you because you didn't play this tune EXACTLY like Mick Fleetwood did in the original track.
I just listened to the original track ... and it's not as sporadic as you might think. Mick uses the Snare for his fills ... and that is just playing the additional backbeats. Why? Because the Tom Toms are already part of the groove, so by leaving out and adding the Snare drum backbeats, it creates tension and release.
I think JeepnDrummer's suggestion and notation from the live version would work just fine to use, and definitely much easier to memorize if that's what you need to do.
JeepnDrummer and I would call the sections differently, which isn't really a surprise because it's subjective. What he calls another Verse, I would call a Pre-Chorus because it sets up the Chorus and has a repeating lyric, unlike the Verse.
Here's what the original recording has for the Snare drum:
Introduction: When the drums enter (bar 5 of the 8 bar introduction) there's one full bar of Snare backbeat on 2 and 4; the remaining 3 bars have the backbeat on 2.
Verse 1 (8 measures) ... Snare backbeats on 2.
Pre-Chorus (8 measures) ... Snare backbeats on 2.
Verse 2 (8 measures) ... Snare backbeats on 2.
Pre-Chorus (10 measures) ... Snare backbeats on 2 & 4.
Up until now ... seems pretty normal to me. The only thing that was different was the very first measure of the drums entrance.Chorus (16 measures + 2 measures extension) ... Snare on 4 (3 measures), Snare on 3 (1 measure

), Snare on 2 for the remainder of the Chorus with exception bar 13 and 17 which has Snare on 2 & 4 ... and bar 18 just plays a downbeat on beat 1.
Verse 3 (8 measures) ... Snare on 2 & 4 (1 bar), then on 4 for the remaining 7 bars.
Pre-Chorus (10 measures + 2 measure extension) ... Snare on 2 & 4
Chorus (8 measures + 2 measures extension) ... Snare on 4 (3 measures), Snare on 3 (1 measure

), Snare on 2 (4 measures)
Chorus (8 measures + 2 measures extension) ... Snare on 4 (3 measures), Snare on 3 (1 measure

), Snare on 2 (4 measures)
Chorus (8 measures + 2 measures extension) ... Snare on 4 (3 measures), Snare on 3 (1 measure

), Snare on 2 (4 measures)
Solo Chorus (and fade) ... Snare on 2 & 4
All of the last three Chorus' are the same, in fact there's only one other Chorus in the tune and that's the very first Chorus. It's a bit different in the latter half because it's extended; it doesn't repeat 8 measures.
In the last Chorus of the tune, the Guitar starts to solo in the last 4 bars, so from what I call the Solo Chorus (to fade), Mick goes to 2 and 4 on the Snare drum ... and even occasionally plays 2 AND on the Snare, which is more of an embellishment or fill than part of the groove ... even though it fits in the groove.
Notice how Mick consistently plays the Snare on beat 3 of the 4
th measure of the Chorus? You see, it's thought out ... it makes sense ... it works ... and to me ... it's brilliant.
I'm not suggesting that YOU play it like this. I simply wanted to address that his drum part was well thought out and was not some random thing he did because of a "substance".
When I first moved to Nashville I was working with a cover band that played casinos, weddings, bar mitzvahs, dog fights, etc. This was the first time I had learned to play "Rhiannon". When I did, I always played it like the original recording with exception to the Solo Chorus because I was reacting and interacting with the soloist. I always kept the persona of the tune in mind however.
Since you have to learn/play this tune so quickly, you just need to do whatever you need to do. JeepnDrummer's notation is probably the easiest and quickest to learn. I just think the original recording is unique and very cool. It makes sense (to me) and love the creativity and artfulness of the part. It's not the norm or cookie-cutter, which makes it standout all the more.
EDIT: I just watched the live performance. The lyric is different in those "Pre-Chorus" sections, so I can see why you would call them Verses ... even though the music is different. No worries.