You can "call BS" all you want, but the question is whether EC 261/2004 applies and if it does, whether he is entitled to EUR 600 per person for the delay. This isn't one of these customer service gestures where they toss a couple of miles your way.

I don't think that this is murky at all. EC 261/2004 does apply, but there is zero compensation due. For a 5-hour delay, LH should have provided OP with some duty of care such as a meal voucher, although it is not apparent to me that it got to this point.

OP really has two approaches and needs to make a choice. If he makes an EC 261/2004 demand/claim, the matter goes to compliance and is dealt with as a strictly legal matter. OP may see a small reimbursement for food ($15-20). On the other hand, if this is made as a CS complaint, OP may see some miles or a credit of some kind. It won't be large, but it will likely be something.

Water under the bridge, but MCT does not mean Sensible Connect Time. Even on a perfect day, this is not a good idea at ORD unless you have no other options and an essential meeting on the other end of the journey.