Dice for Accumulative Hits

Recently, an acquaintance of mine asked a question about original, pre-Greyhawk OD&D (1974) for which I had no immediate answer: how are hit points determined when a character gains a level? That may seem like a very simple question, but consider the following chart from Men & Magic:

If you look at the second column, you'll see there's an uneven progression of "dice for accumulative hits" – 1+1, 2, 3, 4, 5+1, etc. Though the chart above is for the fighting man, both the magic-user and cleric charts are quite similar in this regard, which is why I was asked the question about how hit points are determined upon gaining a level.

If the player of a first-level fighting man rolls 1d6+1 to determine his character's hit points, what does he do when his character acquires the 2000 experience points necessary to gain level 2? How many dice does he roll and add to the total? OD&D's rules are not especially clear on this point, as we can see:

The example in the text is rather unhelpful as it does not describe the process of rolling additional hit points upon gaining a level. Instead, it simply presents how to roll the hit points of Level 8 fighting man divorced from any other context. 
Empire of the Petal Throne was first published in 1975 and its rules are clearly a variant of pre-Greyhawk OD&D. Consequently, when I have some question about how the rules of OD&D are to be interpreted, I often take a look at EPT. There's no guarantee that EPT's presentation is necessarily representative of the original intention (if any) of OD&D's rules, but, if nothing else, they usually offer some insight into how one person chose to interpret those rules, which is better than nothing. 
In this case, EPT suggests that, upon gaining a level, the player rolls the number of dice prescribed by the rules and totals the result. If the total is higher than his character's previous hit point total, the new total is used. If it's lower, then the previous total is retained. This approach makes a lot of sense to me, since, among other things, it helps to ameliorate bad rolls for hit points over time (provided the character survives, of course). It also provides a simple way to deal with the uneven progression of hit dice. Whether this approach is what was intended in OD&D, I simply have no idea.
Of course, it's possible I'm simply missing something very obvious or that this topic has been well explained elsewhere. If so, I'd love to be corrected, since it's a question that really stumped me when I was asked about it. Back when I was playing OD&D in my Dwimmermount campaign, I had already come under the sway of the EPT interpretation and made ready use of it. Later, we adopted Greyhawk's one additional hit die per level approach, so I never had to grapple with this area of ambiguity. 
Thinking about it now, I can't help but assume it's a topic that's been examined thoroughly by better exegetes than myself, but perhaps not. Please let me know what, if anything, I've been missing in the comments.