Our condo complex has three very large Mexican Fan Palms that are dripping sap and shedding seeds that are very sticky. Our parking lot is coated in these seeds, they get tracked in and stick to everything. The sap has ruined my car cover (better than my paint, right?) We've lived here for a long time and this has never happened before, at least to anything near this extent. Anyway, what is causing this mess and how to we prevent it from continuing?
The Palms most likely have a scale insect infestation, and it's been a particularly heavy infestation this year, which would explain why there's so much of a problem this time round.
The difficulty is treating the scale insect, because you describe the trees as large; horticultural oil or neem oil sprays will help, but repeated treatments will be necessary, Whether it's possible to carry out the treatment, I don't know, it will likely require a determined person, a long ladder and a face mask, but more information here (although its aimed at palms as houseplants, the same problem occurs outdoors in areas warm enough to grow these outside) https://www.gardeningknowhow.com/houseplants/palms/sticky-palm-tree-leaves-treatment-for-palm-scale.htm
The other (less likely) possibility is a problem with the trunks, namely, a bacterial infection, but you should be able to see that quite clearly just by looking - there will be dark areas with obvious oozing from the trunks.