This leaves only one tiny little problem --- predicting the highest price of the day before the day is over.

Any suggestions for doing this?

If you can't do this; if you sell too early or too late, your return will potentially be a lot less than picking the high price after the fact.

In other words, the stated returns are maximized assuming perfect clairvoyance --- which no one has. Basing return on closing price assumes zero clairvoyance --- which the average person has --- and is thus a more realistic measure.

The best thing you can do is leave the idea that you will time it correctly. Take profit when you are comfortable. Feetr provides stocks almost every day and, to me, the goal is compound interest.

The metrics are as they are because, right now[0], there are no better options to validate how Feetr performed. These values are, like you say, theoretical maximums and have not been matched by humans in almost a year. You get the top every so often but not consistently.

However, I wouldn't say that this makes the service less useful than people think. I have made 700% returns and this allowed me to quit my job and work on Feetr full time. Other beta testers have made more than their salary using this.

[0] As above, there will be an investment service offered at some point