Nonsens
You guys are cutting a hair in two. If you want to do that then you have to be logical and include the vertical component of the wind as well. The only way to resolve this problem is to take into account the change of drag with speed and the change of thrust with speed, and if you want to be precise, also the change of TAS with altitude at constant IAS. Having said so even the ADC change the IAS as a function of AOA. Some ADC take this into account and some don't. Is there a solution to your question? Yes there is. If all relationships between the variables are known you can solve the equation. So what I want to say is: don't worry be happy and keep it simple or you are going to stall. Now what are you going to do if ATC asks you max angle of climb while climbing in a increasing headwind while at the same time they give you a radar vector that swings you 180° around?