I’m pretty sure that if you use the “Add Batch” functionality at upper right on the place checklist page (example for Nevada) you can overwrite existing values for Establishment Means and Occurrence Status for taxa already in the checklist. (It has been a while since I tried this, but it’s worth a try…)
If it is a long list, I recommend scrolling to the bottom left on the checklist page and Download the list as either CSV or Taxonomic CSV. You can then
sort and eliminate the taxa you are not interested in,
edit Establishment Means and/or Occurrence Status for the remaining rows,
delete all columns except taxon_name, description, occurrence_status, establishment_means (be sure to keep them in this sequence),
delete the header row (column names),
save as a new CSV file and use that as input for the Add Batch function.
EDIT: Occurrence Status will not overwrite initially, but you will have the opportunity to batch-edit Occurrence Status (and Establishment Means) during the Add Batch process.