The hospice medical director recommends anticoagulant therapy rather than surgical intervention for Helen, who has a terminal illness. The anticoagulants may provide relief from her DVT and allow for a more peaceful dying process, while surgery could prolong her suffering without changing the inevitable outcome. The medical director believes Helen's wishes should be prioritized, and that attempting anticoagulation first without surgery respects patient autonomy and avoids unnecessary pain and suffering at the end of life.