GAMEPLAY - Jax loses ad on his q when buying sterak's gage

Pretty simple. As the title explains, when purchasing Sterak's gage, Jax loses ad scaling on his q skill. I haven't checked if he loses ad scaling on his e or on the armor of his ult but imagine it may be the case. My initial guess was that it has something to do with the interaction between Sterak's gage base ad percentage increase and Jax's total ad but I don't know. It may be the case with other champs too. Worth checking.

Please solve this as I'd like to buy Sterak's Gage without losing ad scaling on skills. Thanks yo!