Sequestration of plastic in landfills seems to be the best option we have right now for plastic waste disposal. Even then, more focus on proper encapsulation before it goes in is needed. Even simple initiatives like EcoBricks (https://www.ecobricks.org/) helps ensure more permanent sequestration in ways that look likely to reduce the risk of eventual environmental damage.
We also need more focus on diversion of materials before landfill. Right now an enourmous amount of compostible organic waste, e-waste, and metals are sent to landfill because nobody is willing to bear the cost of diversion. IMO material disposal cost should be borne by the original producer (see the EU WEEE regulations for a good starter on how this can work). This incentivises sustainable choices from the very start of a goods life cycle, rather than how it currently sits as an afterthought.
It's not just island nations either - A great portion of humanity lives close to a coastline and waste is generally interred in proximity to where consumption occurs. Physical damage is not the only consideration - Any situation that prompts power interruption, water damage, or reduced access to the site puts a landfill site at risk of incident. In the US the EPA considers there to be significant risk of these events and has had it in their sights for at least a decade: https://semspub.epa.gov/work/11/175853.pdf
Assuming that sea level rise is just a matter of adjusting the shoreline in accordance with topography is also a huge mistake - Erosion increases rate and begins occurring in places it didn't previously. Storm surges and king tides bring surge water to higher points that ever before, and intrusion of saltwater into landfills poses far higher risk of leaching than rain, river, or aquifer.
The underlying problem is a changing risk management landscape - A decision to site a landfill on a once-in-300-years flood site may be taken, but when that assessment is later revised to once-in-100 years, you're faced with either rolling the dice each year or pulling funding out of your ass to relocate. Repeat the gamble at a global scale at many thousands of sites, the overall odds look very bleak.
"Landfills could hold only so much, and people were concerned about burning toxics into the air — but the Pacific Ocean seemed a good alternative. Explosives, oil refinery waste, trash and rotting meats all went into the ocean, along with beryllium, various acid sludges, even cyanide." [1]
Companies were dumping and putting out of site. Much harder to burn it and avoid getting caught.
Third world countries are also taking first world trash and then dumping massive amounts into rivers and the ocean.
Cleaning up the ocean is a hell of a lot harder than cleaning up the air or the ground.
[1] https://www.latimes.com/projects/la-coast-ddt-dumping-ground...