In my opinion the approach by which D'Ooge teaches the third declension, i.e. deriving the nominative and stem from each other based on phonology rules, works very well for some languages, but not for Latin. These ways of predicting nominative and stem from each other in the third declension are quite interesting and can be very illuminating at times, but there are so many sound changes that occur in the third declension that it is almost absurd to ask the student to memorize all the sound changes just to have the ability to make an educated guess at the nominative/stem, which will still often be a bit off. In fact, if the student memorizes the nominative and genitive (or other stem-revealing case), most of these patterns will start to become apparent, and at that time the student may go back and formalize the rules if they are so inclined.
I can see two possible ways of doing this.
(1) Internalising the nominative singular form, the stem, and the gender.
(2) Internalising the nominative singular and plural, and the genitive plural.
The traditional method is to memorize the nominative singular and genitive singular, but I suppose memorizing the nominative singular and genitive plural would be a little more informative. In either case, you still have to memorize gender and, in i-stems, to what degree the noun retains/inserts the i.
I would not recommend memorizing the nominative singular and plural as well as the genitive plural. While the nominative plural would tell you right away the gender of neuter nouns, it would serve no added purpose for the masc/fem nouns.
Third declension neuter forms differ significantly from the masculine / feminine forms in both the consonant and -i- stems. What information should we internalise in order to reconstruct the entire declension and determine the correct gender to render modifiers in?
If you do intend to use D'Ooge's approach and this matter of the neuters is grieving you, perhaps this will help you:
neuters of the third declension use the stem for the nominative
. The vowels sometimes get weakened, (caput, capit-; flumen, flumin-) but the consonants generally remain and the vowel positions are still filled by vowels. For neuter i-stems the final i of the stem either drops (animal, animali-) or is weakened to -e (mare, mari-).
flebile nescio quid queritur lyra, flebile lingua murmurat exanimis, respondent flebile ripae