Highly social 3 Year old is disruptive at Montessori school

My son is 3 years old and has been attending Montessori preschool since before he was 2. He is very bright, particularly in the area of language and is extremely social.  He will often strike up conversations with neighbors, is polite, asks for things and says please/thank you unprompted.  He follows directions extremely well, his comprehension is high, he flourishes with one-on-one attention, verbal praise, and loves being around other people.

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However, he has recently been getting into trouble at his Montessori preschool for the past few weeks, despite attempts from us and his teachers to address his behavior.  The children are expected to work independently for a period of time each day (Montessori time), but our son has been "bothering" other kids, touching them, and grabbing their work.  I strongly believe he is doing this to get attention, which he craves, along with his desire to talk and socialize. This directly conflicts with Montessori principles of independent work, the teacher "observing" the children (rather than interacting with them). His problems have only occurred during independent work, no issues during guided activities, circle time, outdoor time, etc.

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At home he will get engrossed in independent play/work (building, art, vehicle play, etc.) but only if I am present in the same room and with frequent verbal check-ins every 2-3 min ("Wow, look at that cool house you built!" "I like the colors you're using.", etc.) or if I work alongside him. That's obviously not possible at school, and is not in line with the Montessori concept of independent work. Any suggestions on how to handle this, either at home or with his teachers at school?