My plan is to keep hitting singles consistently and then just keep increasing the size until I'm happy with the numbers that come out. Does this seem reasonable?
Yes, understood. Say you have an average pnl of $500/trade. Would you (for example) double size so that average becomes $1000/trade?
Entirely different league and game but 800 pound gorillas like Marty Schwartz and Lew Borsellino used to trade hundreds of the big contract in the S&P pit. Now THAT'S size.
I would be lost in the Pit but you can get a good idea by reading Marty's book...Pit Bull, good stuff.
They had a way of reading momentum waves and would scalp in and out of large positions many times a day....not for the faint of heart, but they made millions.