If we look at the beginning sequence /mʌŋ/ (‘mV9*’ in the search code for the MRC Database), then we get the following much shorter list: MONGER; MONGREL; MONKEY. But something is wrong. Where has MONK gone? Unfortunately the compilers of the database seem to have changed their minds about the transcription symbols, and at one stage ‘N’ was used for /ŋ/, though ‘N’ was later used for all nasal sounds (so /m,n, ŋ/ in English). MONK was transcribed with N, as too were many words derived from MONKEY. This reveals another hazard of using databases! But let’s put MONK back in. So our cohort given the first three phonemes (and leaving out the related words) is MONGER; MONGREL; MONKEY; MONK. On this basis we can say that the Uniqueness Point (the point at which the word becomes distinct from all others) is the /i/, since this is MONKEY becomes distinct from MONK. Note by the way that a common mistake in this sort of exercise is to think about how the words are written, and not about how they sound.
For swing, the uniqueness point is also its final sound, the /ŋ/ as this is where it becomes distinct from swim, swish, etc.
In the sentence All the children loved watching the long-tailed monkey as it started to swing through the trees we are likely to find that the recognition points (RPs) are earlier than the uniqueness points (UPs) determined above. Assuming a monk cannot be long-tailed and is unlikely to be watched by children, then the RP here has to be earlier, at the /k/ (which distinguishes it from musk-rat and mongrel). If a mongrel is unlikely in a broader context (e.g. a visit to the zoo) and assuming that a musk-rat can be long-tailed, then the RP may be as early as the /ŋ/ of monkey. For swing, however, we find that the RP does not differ from the UP, because there are other compatible verbs – for instance, a long-tailed monkey could start to swim or to swish its long tail.