Accidental kitchen fire triggered sprinkler that flooded the rental apartment. How to manage repair costs going above insurance coverage?

Disclaimer: I am new to US (relocated 4 months ago) and dealing with property repair for the first time so pardon my basic knowledge.

I relocated internationally to Washington (US) 4 months ago and rented an apartment. I took 100k liability coverage renters insurance as asked by property management for lease. Few weeks ago, I had an accident during cooking that started small fire on electric kitchen stove top. This kicked off fire alarm (for my unit and full building) and started sprinkler located in kitchen. Sprinkler water extinguished fire within couple of seconds and I then came out of building due to emergency sounds. Fire truck came within 5 mins and I informed them of the incident. Fire men went to shut off sprinklers but by then, complete unit was flooded. I am living on 3rd floor and water from my unit also went into unit below me as well as to 1st floor commercial dental office. Fire men diverted my unit's water to washroom and removed toilet seat to drain water from its pipe.

Property management visited the apartment after ~1 hour and called in another company (ServPro) to start installing big fans and dehumidifiers. After running fans and dehumidifiers for few days, ServPro provided damage report saying complete kitchen will need to be reinstalled, flooring will be removed and flood-cuts will be made into walls. I started my insurance claim process and they sent in inspector to assess the damage. I relocated temporarily on my own since my insurance only covered $1600 for additional living expenses. The apartment became inhabitable and I was asked to either a) break lease (2 months rent penalty), b) Move into different unit becoming available after 15 days (1 month rent penalty), or c) Continue paying rent in ongoing lease until repair is done. Property management provided repair timeline estimate of 3-4 months and mentioned that repair costs are going to be more than insurance coverage (~150k).

If am looking for guidance/options to manage repair cost payment above my insurance coverage.