My personal opinion
As someone who used to main Tristana in Season 4 and tried to main her again Season 5, I would have to agree that her nerfs are indeed a bit harsh. I feel that she has been removed from the whole hyper-carry role and thrown into a weird support-carry role. Her laning is extremely harsh with the lowered AS, and her range doesn't help her much to trade since other carries have more reliable ways to trade (Buckshot, Tumble, Jinx Q, etc). Although Tristana has self peel with her Ulti and Rocket Jump, there isn't much reason to pick her over Jinx who does just about the same thing, but with more damage and persistent attack speed, and is even stronger in teamfights.
Furthermore, I believe that in order for Tristana to excel at all in-game she has to either snowball extremely hard, or rely on her teammates, so that she can push turrets as a 5man or split push while 4 others pull pressure. Due to Tristana's lack of AS during laning phase, she loses tremendous amounts of damage since she can't properly stack her E unless the enemy just decides to stand still. Compared to Jinx, there isn't a whole lot of reason to pick Tristana, since Jinx is technically safer with longer range, MS buff on kill/assist, and also her slow and traps. Jinx has basically taken over the role of Tristana's hyper-carry role leaving Tristana to be in a bit of a weird spot, since she doesn't really hyper-carry, and she's not really a support.
Moreover, in order to remedy this, I feel that Riot should just revert the AS nerfs or at least buff her AS, but keep the range nerfs in order to bring Tristana back to her hyper-carry role. 670 Range is plenty for a champion like Tristana that can escape with Rocket Jump or knock multiple enemies away, and the lack of range may also act as counter-play as she will have to be a lot closer to auto-attack enemies. Furthermore, this would make Tristana a great contender with Jinx, as Tristana would offer more turret pushing power with her increased AS whereas Jinx would offer more Range and Damage.