Liland,
The short answer is keep them both, either are correct.

The long answer is an explanation of both tradition & the notation you're seeing. (Examples drawn mostly from online Southern Harmony)

The 'rule' is that internal repeats are always observed & repeats at the end are optional. The internal repeats usually are for repeating the next section of words to the same music, like in your Beach Spring copy. The final repeat is the option of the leader.

In practice the terminal repeats are usually just done on the last verse. They are almost always done on fuging tunes. The only time I've seen them omitted in a fuge is because the leader lost track of if it had been done or not. For a tune that's not a fuge, like Cookham, it's up to the requestor/leader. What you should do in only very rare cases is use the repeat on every verse. Leaders will sometimes also put repeats in that are not written, especially if there's a chorus. My rule of thumb is do what comes naturally & feels right at the time. It's not always the same.

When coming from a choir/sing as written frame this seemed like it was strange esoteric practice. It fell into place for me in a 'folk' frame at a Welsh hymn sing I went to where the director was soaking it up & at the end of a hymn kept right on going. Without prior alert & barely missing a beat the singers & the organist knew just what to sing over again simply because it comes so naturally. Think of Cwm Rhondda, you just know to repeat the last 2 lines. It's even more obvious with chorus songs. Then pay attention to any kind of folk performance & notice how often final verses, final choruses or final sections are repeated.

On to the notation. I can tell you're not using a James, Denson or 1991 edition for your source. Is it a reprint of the 1859? I started noticing the missing repeat marks at the end when I started using the Cooper edition, which also omits them. If you look at any of the older shape note books, you'll find that they are just not present. At best there will occasionally be a 2nd ending (as in your Cookham copy). If you really want confusion try to figure out the internal repeats for Easter Anthem. The interpretation of the repeats supplied by ccel (repeating the lines before the : rather than the portion after), is not the way we do it. Then try Huntington!

I think either the 1911 (James) or the 1935 (Denson) editions must have added the terminal repeats. I don't have a copy of the 1859, but, I've also discovered that we have many repeats that are not present in the Cooper ed. or the Southern Harmony. Beach Spring is a good example where the 1991 ed. has a repeat of the 2nd half. Coronation is another. Many of the fuging tunes lack repeats in Southern Harmony that are in Sacred Harp.

Now is where I go into pure speculation. It would appear that James added the repeats that were commonly done when the revision was done. Just from the practice of singing, I'm becoming increasingly convinced that a final repeat is just something that comes naturally. In that context, one does not need a terminal repeat to tell you to repeat the last section. One might, however, need a repeat if the point to return to seems ambiguous. One might also be needed if the repeat changes the counting a bit so a 1st & 2nd ending would complete the measures.

I guess a final note is that repeating has a lot to do with the feel of the song at the moment it is being done. Not only is the repeat optional, but if it's really kicking the repeat may be done several time. One good example is Hallelujah. There's no repeat in Walker's original. Later editions of Sacred Harp do have a repeat & I have done the chorus 3 times when it was really hot.