My comments -

Density altitude computes to at least 3800 ft.

Maximum TOGW at SL = 3650 lbs. His TOGW computes to 3638 lbs.

Max SL HP is 300. His max available TO HP computes to 285.

Due to the lower HP and air Density ratio combination, his max propeller thrust available was less than 90% of SL rated thrust.

In effect, his maximum rate of climb out of ground effect was NEGATIVE!

Hmmm, not exactly sure how you arrived at a negative climb out rate. Not necessarily doubting you as this reads to me like some kind of theory from aeronautical engineering but could you expand a bit and show your work.

In a more practical sense, GA aircraft are delivered with takeoff and landing distance charts in the POH that a pilot is supposed to use to calculate take off distance needed. The charts are normally designed so that no complicated math is needed. Taking into account wind direction and speed, density altitude, take off weight, slope of runway, and any obstacles at the end of the runway, a pilot can derive safe takeoff distance using these charts.

It is suggested that pilots add anywhere from 20 to 50% to the takeoff distance pulled from these charts to account for the fact that these charts are produced under the best possible conditions (new engine, test pilot skills, properly inflated tires, etc.). Therefore, if the takeoff conditions resulted in a chart-derived TO distance of (for example purposes only) 2,700 feet, one would add a fudge factor of 540 feet up to 1,350 feet, or a total distance of 3,240 to 4,050 feet of runway distance needed.

A tip I read from a well-known mountain flying guru is that if you reach about 70% of takeoff speed within 50% of the runway, continue the takeoff. Otherwise, abort. Of course, this requires a pilot plan the takeoff enough to know where the halfway point of the runway is and have the confidence enough to abort with a plane full of passengers wanting to get to their golf outing.