I vote for the matte finish - and in future consider painting your palm trunks. Yes, looks good but a little more 'prep' work and that matte finish are very worth the end result. Though I like the 'it just rained' excuse.
If you can find them in your zone of the world, floral decorating spray paint can be a great source - always seems to go on more as a mist than an even coat which is exactly what is needed. Beware of high pigment paints for this project, though - I wouldn't dare use Montana brand paints (I do use them, just not for this).
Looks very good, however. Though, again, your nice basing does conflict with the shiny plastic - another argument for the matte.