I do not, I only have one 16" large frame and it's a 308 and I specifically avoided midlength and bought a barrel because it was an intermediate length. It is gassed well and is smooth, but I wish it just shot a little better. It's 1 to 1.5moa gun. Part of the reason I have started to avoid off the shelf large frame barrels. The ideal mix of characteristics become really restrictive. Additionally you see people on here talking about issues with midlength gas systems and asking for advice when their gun is tearing up brass. A person could even argue that midlength on a 16" 223 AR tends to be harsh; in comparison to intermediate lengths. It's like the carbine vs midlength debate for 12.5's and the hybrid has lengths manufacturers have come out with specifically for 12.5" barrels.
And then on top of all that, are you planning on running it braked, suppressed, or do you have ideas of 50/50 mix? I think best case scenario a midlength functions but is polarizing. Whereas an intermediate length will provide a little flexibility in the operating system.