Are you putting risers under the supports under the bed as well? Even queen beds have one, how many do king beds have? And definitely take the bed apart and check that it is put together properly and all bolts are good and snug. Sometimes bolts loosen up in use even if they were nice and tight. If you suspect that's going on use something like loctite to keep them snug.

Maybe going for a frame like this from Amazon would be steadier than using your existing frame.

However, don't buy anything until you are completely done purging your entire home. It's possible you won't need to use that space and it would be wasted money buying organizing devices. When I bought my 9" off the floor bed I expected to use it for storage but ended up getting rid of half my storage furniture.