You know for the legs you could just get some that are made backwards and have them mount on the inside of the corners between tables instead of the normal way on on the outside of the corner. Then each cabinet can stand on 3 legs while moving/assembling and when together would have 4 supporting the "center" section of the cabinet. Then you just put some bracket inside the cabinets to lock them together.
my ideal is assuming that the cabinets will be assembled first then the play fields put in after.