"surely a speed closer to the best rate of climb (the speed where the excess of thrust available is at a maximum)"
You really need to be careful that you don't confuse the most fundamental of differences between best rate and best angle.
In a GPWS encounter, you want best angle of climb without any question. The maximum "up" for the minimum distance.
For a windshear encounter, I would be generally inclined towards Stick Flyings idea. Best rate would be much better as it will give you the best protection against a downdraft.
BUT!!
At the kind of speeds that you are going to encounter windshear, best rate is not an option. You are way too slow already. Best rate of climb speed in a jet is significantly higher than best angle. The most suitable option remaining is to trade any excess speed over and above best angle of climb speed and turn it (albeit it briefly) into improved climb performance. This way you maximise the short term capability of the aircraft to outclimb the shear or downdraft even though it's long term climb rate may have been adversely affected. If you can not trade enough airspeed for an improved climb, well it's just not your day.
The majority of machinery I have seen has generally the same principle. Trade airspeed for climb ability all the way down to the minimum safe airspeed which is usually to stick shaker or Alpha Floor.
Remember, your immediate concerns are short term.