Yes, you can either by direct collecting by hand, or by sifting litter and soil in the studied habitats. The sifting trays are very efficient for capturing soil fauna.
(1) Fast moving jumping spiders by electronic rechargeable aspirators (work like cleaning vaccums) provided with a collecting chamber, focus inside the fronds' bases, (2) Web-spinners through hand picking.
While hand collecting works well on the trunk, I am not aware of any studies that have compared the spider fauna on the lower trunk with that on the middle and upper trunk. This comparison would be interesting. I would suggest that you find a method to gain access to the leaves (cherry picker) and the fronds can be shaken into a net as well as hand collected. The base of the fronds and fruiting areas could be collected by one of the people who regularly climb the trees to pick the fruit - again hand collecting as well as shaking any materials into a net will yield some spiders.
A way to monitor, and obtain some quantitative data, is to use a modified "pitfall" type of trap on the trunks, comparing sides, tree location, trunk heights, etc. A very simple form of the trap is included in the website link.