The Bodhisattva vow itself blocks the person from attaining nibbana or at least stream entry. That's the world nature. In fact, once another Buddha declares a bodhistva as a future Buddha, it means he will only attain nibbana when reached buddhahood. Nothing else
I think that Mahayana literature teaches that becoming an Arhat is a temporary rest, for example:
Mahayanins are urged to instead take up the path of the bodhisattva and to not fall back to the level of arhats and śrāvakas. Therefore, it is taught that an arhat must go on to become a bodhisattva eventually. If they fail to do so in the lifetime in which they reach the attainment, they will fall into a deep samādhi of emptiness, thence to be roused and taught the bodhisattva path, presumably when ready. According to the Lotus Sutra, any true arhat will eventually accept the Mahāyāna path.
Or from The Jewel Ornament Of Liberation by Gampopa,
III. HEARER FAMILY
The family of Hearers consists of those who fear samsara and yearn to achieve nirvana, but who have little compassion. It has been said:
One who is afraid upon seeing the suffering of samsara
And yearns to achieve nirvana
But has little interest in benefitting sentient beings—
These three are the marks of the Hearer family
IV. SOLITARY REALIZER FAMILY
The Solitary Realizer family includes those who possess the above three attributes and in addition are arrogant, keep their masters’ identities secret, and prefer to stay in solitary places. It has been said:
Fear at the thought of samsara, yearning for nirvana,
Little compassion, arrogance,
Secretive about their teachers, and enjoying solitude—
A wise one should understand that these are the marks of the Solitary Realizer family
So these two families, the Hearers and the Solitary Realizers, engage in their respective vehicles and even though they achieve the results of their practices, these results are not the final nirvana. How do they abide when they achieve their fruits? They maintain unafflicted states of meditative concentration, but those states are based on the psychic imprint of ignorance. Since their meditative concentrations are unafflicted, they believe that they have achieved nirvana and remain that way.
If their states are not the final nirvana, then one might argue that the Buddha should not have taught these two paths. Is there a reason the Buddha should teach such paths? Yes. For example, suppose great merchants from this Jambudvipa are traveling the ocean searching for jewels. After many months at sea, in some desolate place, they become completely tired and exhausted and think, “There is no way to get the jewels now”. When they feel discouraged and prepare to turn back, the merchant captain manifests a huge island through his miracle power and lets all his followers rest there. After a few days, when they are fully rested and relaxed, the captain says, “We have not achieved our goal. Now we should go farther to get our jewels.”
Similarly, sentient beings without courage are frightened when they hear about the Buddha’s wisdom. They believe attaining Buddhahood is a great hardship, and think, “I have no ability to do this.” There are other people who are not interested in entering the path, or who enter the path but turn back. To counter these problems, Buddha presented these two paths, and allows them to rest in these states.
As said in the White Lotus of Sublime Dharma Sutra:
Likewise, all the Hearers
Think that they achieved nirvana,
But they have not achieved the final nirvana
Revealed by the Buddha
They are only resting
When these Hearers and Solitary Realizers are well rested in those states, Buddha understands this and encourages them to attain Buddhahood. How does Buddha encourage them? He awakens them through his body, speech, and wisdom mind.
The question is illogical & non-sequitur because the Pali in SN 13.1 does not contain the word "lives". Instead, SN 13.1 appears to be about the "breakthrough" and seems to be explaining the stream-enterer has seven more breakthroughs (of fetters) at most.
Therefore, if reincarnation really existed (which really does not) and if SN 13.1 is understood as suggested above, the stream-enterer could have billions more lifetimes because there are seven more fetters to break at most (rather than seven more lives).
In short, there is no contradiction because the Mahayana Bodhisatva has broken at least three fetters; thus knows the path to end suffering, to share with all sentient beings.
As for Mahayana, it is a different religion than the Pali suttas, even though Mahayana ideas were obviously influenced by the corruptions that arose in Theravada, such as the Jataka Tales.
This said, the Pali suttas do not ever depict a stream-enterer reincarnated in the human world again. All stream-enterers, after they end stream-entry ('death') appear in a pure abode, where final Nibbana is attained. This again shows why SN 13.1 does not mean 'seven more lives'.
To conclude, the Buddha-Dhamma is said to be visible here-&-now & verified by those with vipassana. Minds that have real vipassana (seeing anatta) do not believe in reincarnation. The Pali keeps the supramundane & mundane distinctly separate (refer to MN 117). Trying to reconcile two superstitions (misinterpretation of SN 13.1 and Mahayana Bodhisatva belief) is not Buddha-Dhamma but, as described in SN 23.2, the activity of children playing with sandcastles.
Just as when boys or girls are playing with little sand castles: as long as they are not free from passion, desire, love, thirst, fever & craving for those little sand castles, that's how long they have fun with those sand castles, enjoy them, treasure them, feel possessive of them. SN 23.2
[Note: This is a gift of Dhamma, not meant for commercial purpose or other wordily gaining (possible not good for those desire for becoming a Buddha and not firm in it.]
Usually/practical by avoiding to listening the Dhamma of a Buddha and taking care of not gaining wisdom or right view. So avoiding the three Juwels as good as possible, if still present in the world.
Maybe some food for benefical thought: A Bodhisttva is a member of the Sangha?
Here in Cambodia, people who have not really taken refuge into the Juwels, so if speaking about people not explicit Dhammika, are called "Buddh(a)bodhisatt(a)".
Since the root of stream-entry is right view, this has to be avoided, if one wishes to become a Buddha. If such is possible, having been touched by the good Dhamma... who knows...
Of coures it might be, that seven lives as a certain devas lasts as long as a world period. Did not made more researches in this regard.
This might be also useful for those desiring becoming a Buddha: Bodhisatta Path Answers of questions
And a nice Bodhisatta-story: The Spiritual Partner
Sotapanna (stream-enter/wisdom throw hearing) is connected with the four Noble Truth. If, when a person heard the 4NT, understanding them, not mental cognitive defect, can than, later, take on Bodhisatta-vows and avoid stream entry: my person doubts. He/she will gain the path latest with death. So possible a wasted time with a lot of pain, struggle and suffering, if having heard and understood the Dhamma, to try to avoid entry afterwards.
Some say there is a point in the Vipassana-states, where one might have gained some good insight, and where one is able to decide. A hint on it is in the 'Question and Answer' link.
It might be therefore (for a desire of becoming a Buddha), good to take on the vows before hearing the 4NT and understanding them, e.g. not taking refuge into the current Buddha, his Dhamma, his Sangha.