Is there a way to send a MOC order in the last minute of trading (instead of 10 or 15 minutes ahead of time) and get a good fill trading $50-100k on stocks doing > 100k average volume? Perhaps through a dark pool?
No. Your order will be rejected. I can't think why anybody would want to take the risk of being on the other side of trade.
Only floor brokers can add, cancel or change MOC orders up to 10 seconds before the close. https://www.nyse.com/article/trading/d-order
There are at least 2 brokers that offer conditional-at-time orders, with which you can specify the time for an order to trigger. For example, a few seconds before the close.
I don't like it because it defeats the purpose of moc order which guarantees you same the fill as everybody else. You are assuming the same liquidity as the moc order. maybe yes or maybe no. The plus, maybe, moc orders are filled sometimes a distance from the 3:59:59 price
The question is why? If your intention is to minimize market impact an MOC could see you get slaughtered depending on name a liquidity. Talk to your broker and ask them what liquidity is available to them. Again depending on name and liquidity a couple of ISOs in the last hour or throughout the day. Other choices, but the real question is what is your intent?
IB can send MOC orders to a floor broker until 3:59:25. You need to contact support to enable it. https://www.interactivebrokers.com/en/index.php?f=4103