It sounds like your pallets are the kind with gaps in between each slat - am I picturing that right?
(This idea addresses the planning stage versus already-built beds.)
We have a nearby flooring company whose owner lets my husband get their empty pallets. They're heat-treated, and most of them have solid tops.
By "solid", I mean the top slats butt up to each other and there are no significant gaps.
He's used these for several projects, including a privacy fence and raised garden beds.
Here's a typical solid-top heat-treated pallet:
And here are the simple garden beds my husband built using these pallets:
Hopefully that shows how the soil is contained, and how relatively little dismantling is needed - mostly cutting.
The further bed is about a year old - more weathered.
The closer bed is newly built and hasn't been exposed to much weather yet.
I don't know how common these are, or what other businesses might require pallets without gaps. But they are out there, and you just might be able to find a local source for them.