You left the realm of rules and entered the realm of rulings when you allowed the portable hole to enter the vessel.
In the Q&A Is it safe to bring an item like a Bag of Holding into a Genie Warlock's Bottle?, I make the case that rules-as-written, it is not safe to do this.
The description of the portable hole says:
Placing a portable hole inside an extradimensional space created by a bag of holding, handy haversack, or similar item instantly destroys both items and opens a gate to the Astral Plane.
It seems to me to be a rather straightforward reading of the rules that the Genie's Vessel is definitely a "similar item" - both items create extradimensional spaces inside of small containers. Ergo, bringing your vessel inside the portable hole or vice-versa creates a gate to the Astral Plane.
However, you have stated in the question:
Assume for the purposes of this question that the Genie's Vessel is not a "similar item" for the purposes of the portable hole's destruction clause
My answer to that related question accounts for this:
That said, it wouldn’t be a terrible thing to permit this interaction without the usual consequences, as long as you are prepared as a DM to deal with the shenanigans that might follow.
You have found one such shenanigan. Since your DM has made the ruling that allows for this question to exist at all, it is entirely up to them to manage the shenanigans that result. The trouble here is that it seems you have found a loophole that diminishes one of the limitations on the Bottled Respite feature.
When we find things like this, it should cause us to question the path that got us here. In this case, we know how we got here – we allowed items to interact in a manner contrary to their rules, which is okay. Discuss this with the DM so you can come to an agreeable ruling together.
Keep in mind, the portable hole can only be inhabited for up to 10 minutes at a time, and it is likely that the DM will not allow you to just leave and reenter to reset that timer – another thing to talk to them about.