No, you definitely don't want tazdingo in midrange hunter. It's impossible for the games he saves you to outweigh his poor pressure. Tazdingo is actually way worse than a lot of the cards you "called out" in the context of midrange hunter, even though he's really solid in virtually every other archetype.
We know you have Shredders, chairs, there's no reason to leave them out of any sort of hunter deck. It's a nutty card.
I wouldn't come down so hard on Timber Wolf and Hyena. They definitely aren't used in 100% optimized Midrange Hunter lists, but if you wanted one of those, you could look those up, you know where they are. Both cards aren't awful. Both Timber Wolf and Hyena were used in high level tournament play back in a previous meta, and I don't think anything that has made an appearance in high level tournament play in SOME meta is total garbage.
Core Rager and Gladiator's Longbow are harder to love. It's cool to have opened two copies of an epic, but the longbow is very often an expensive Arcanite Reaper, and there are better options. (1 might be ok, definitely not two) Core Rager is generally worse than Lost Tallstrider based on my experiences trying to dump hand for Quick Shot, and also there's an issue with 4 drops not comboing with Houndmaster very well. If you manage to stick your turn 2 or turn 3 beast, you want to play Houndmaster himself turn 4. If you can't make a beast stick for turn 4, you have to wait until you can play a beast and Houndmaster it the same turn. With 2 drop beasts, that can happen turn 6, which is a decently relevant time. With Core Rager, it can't happen until turn 8, which is too late to be relevant in far too many cases. So decks that use Houndmaster really don't like 4 cost beasts.
Tundra Rhino is just never a 2-of because you don't want to draw 2. 1 might be ok.
Tiger, Spiderbabies, Snake Trap, Flare, King's Elekk, those are some cards you might want to think about in general for this type of list. I would not craft any of them. Midrange hunter is very versatile and it is not so hard to replace cards with alternates.
It is correct that you absolutely need Animal Companion. The card is just too good.
If you are having trouble with Secret Pally, the obvious thing is, run Flare. However, you might not want to craft Flare. Crafting rares is dust inefficient: so dust inefficient, I only have 1 Flare myself, and I have a BIG collection. If you haven't cracked a Flare yet, I would recommend trying Tracking. Tracking can work like the third, or half of the third, Kill Command, which can jump over Noble Sacrifice and Tirion to finish off the secret Pally when they try to stabilize.