Have your characters make art objects.
This is less a solution to some nebulous problem (“what are we gonna do with all these emeralds, Jack?”) and more something extra the party can do to gain a few benefits. Maybe a character can craft luxuries which would be otherwise difficult or expensive to obtain which will help curry favor with an NPC who likes that particular style of item. This also gives idle party members something to do while others are doing off-camera things like training, researching spells, crafting magic items, trawling for hirelings, or consulting sages. It’s also a way to combine coin wealth with gem wealth into smaller packages for even easier transport and salability, with the bonus of adding a little value to the gold in exchange for the expertise involved.
Set a gold limit. say 50 gp/level. A character can spend this much gold on supplies (or just melt it down, whatever, we’re flexible) to make the object. She can also include a number of gems equal to twice her level, regardless of their value. The final value of the piece is the value of any gems included plus double the gold investment (to represent the labor and craftsmanship). If the characters find the raw materials themselves, use the materials’ value for the gold investment. Of course, making an art object is time consuming, and unless your character is willing to build her own jewelry workshop, she’s going to be paying for access to someone else’s space and tools. So it behooves her to save up money and materials for several pieces and then spend a couple of days furiously crafting while everyone else runs errands.
This opens up possibilities for adventure in order to get rare supplies. In the event that your character’s craft grabs the attention of a wealthy patron, you might be commissioned to create a fine work incorporating something like ultramarine pigment. Of course, in your world it’s not just some rock that gets powdered to become an expensive paint – it’s the gems at the heart of giant sea urchins, or moonstones which literally come from the moon. Your patron will do just about anything to have this object before his next soiree; he really wants to upstage his rivals. He’ll even cover combat pay if you just get it done within a fortnight.
And now your characters will be keeping an eye on the things they discover in dungeons. That small, jagged chunk of pure but unworked marble might be worth hauling out if it can be carved into a lucky amulet. Maybe that giant statue you just rolled on your Unreasonably Huge Treasures chart can’t be hauled out whole, but parts of it can be scavenged for new creations.