1031 exchange using a "REIT" like entity between 2 LLCs

[SHAW ALI]

Wanted to know if a 1031 exchange can be done where the selling LLC buys shares in a "homemade REIT" (basically some mechanism for selling shares in an LLC) in another LLC which also holds properties, both LLCs owned by same group of investors. This way the selling LLC can be freed from the timelines to find properties and close deals, using the proceeds that are now parked in the 2nd LLC to opportunistically invest properties without timeline constraints.

Please contact  me if I have not been able to communicate my "newbie"  idea across