Lauzon would be cheaper but I do not think Nashville would move him. I like Middleton but he is not as physical as people think, he would far and away be the Bruins most physical D however and I would love to get him here.
DeBrusk would do it and they could get Duhaime as well who I also like a great deal.
If they do this it would require replacing DeBrusk and I would try to get Frank Vatrano back. Not as good a player as DeBrusk but much more consistent and more physical.
Arber Xhekaj is a young, physical D who would look great here. I would do Merkulov and another pick/prospect or the 2025 first for him as Montreal is suppose to be looking for a first for him. He could easily develop into a 30-35 point D who is a well above average fighter and hitter. He is far and away the most physical of the D's mentioned so far in this post.
College free agents I am not sure but a cheap, quick fix for the fourth line could be Max Comtois who is a free agent play for the Chicago Wolves on an AHL only deal.
Stat line
Cost nothing, if he can't play at an NHL level anymore he goes to Providence. Sign him to a league minimum deal.