If this is the case then why are you trying to micro-manage the way your broker is handling the order? You're basically contradicting yourself... either you want to work the order every nanosecond or you want to forget about it for a week. Which one is it?
I do both...When I am online I will drop till I fill, or I will drop till I am the only one sitting there at my price, waiting for a fill, even if it's for days or weeks at that price. Many times I will come back 1 minute, 20 minutes, an hour, or a day later and submit another price. I don't live to trade... I know people jump me, I get it.
I do both active and passive. I don't use a computer (except for trades). No special hardware or software (except my own research and Yahoo! Finance).
I go with industry leaders for trading (Schwab/Fidelity)...Not Flybynight Brokerage.com. 24 hour customer service...Schwab had 7.13 trillion dollars (assets under management as of August 2022). They and Fidelity are doing it right. I reward them with my business (Also own some Schwab shares).
Do I like everything they do...NO! But, I sleep well at night. Just wish they would tweak their routing a bit. I believe the SEC will step in and do that for them in the next few weeks/months.