The phrase "more unreservedly" implies a level of openness, sincerity or willingness to express oneself without any reservations. Its opposite, "less unreservedly", would suggest some degree of reluctance, caution or inhibition in communication. Some possible antonyms for "more unreservedly" could include phrases such as "with reservations", "hesitantly", "guardedly", "inhibitedly", or "tentatively". These terms would convey a sense of restriction, doubt or lack of confidence, implying that the person speaking is holding back or not fully committing to what they are saying. Ultimately, the choice of antonym would depend on the exact context for which it is used.