I use a variant of this. Rhythmic solfege. It is very effective. I never really got a sense of reading rhythms with numbers and as a result I had to rely heavily on memorization. One day I met a piano teacher who used this method (with different syllables) and I was very quickly able to overcome my hurdles. You are right ot one to learn how to practice these things without a metronome since you really can't always rely on one to follow you through ritardandos and tempo changes.
Don't try to learn the syllables all at once since you would be compounding learning the rhythms and the syllables. Just learn one set of syllables and get used to it it and then keep adding as saying the syllables become automatic.
EDIT: The variant of rhytmic solfege originally posted is called takadimi. I suspect that there are several other names based on the syllables used. Takadimi is just the first google result.