Well… in general the idea is less things in the crate they can chew/ingest to cause obstructions until they are old enough to know/be trained better and not be driven to chew as puppies who are teething can. I'm going to leave it at that and let the more experienced people define it better then I can.
As for the horse stall mats, they're basically thick rubber mats. Some examples are here:
https://www.rubberflooringinc.com/horse-stall-mats.html
https://www.farmtek.com/farm/supplies/c ... _wall.html
They come in different varieties but they are more comfortable to stand/lay on. When I tried it with Hendrix he managed to chew a hole starting at the top in a corner. We had a large piece we cut down to size. Not saying every dog will do this and Taki probably wouldn't be able to chew a hole through it. It took him about 45 minutes to get a nice hole. I blame the sharp puppy teeth he had that have now thankfully been replaced. Now, there is also a very good possibility we got a defective or lower quality mat, as I used to ride horses and never saw a rubber mat get destroyed that easily. I would and will try it again as he gets bigger. If you have horse friends, you could see if they have any old or maybe extra pieces lying around that you could test Taki with. Or maybe put her in an empty, clean stall and see what she does.
As for the vertical space… for the dog to be comfortable you want a crate the dog can sit up and stand up in without having to crouch. It's kind of the equivalent of us sleeping in a recliner or an airline seat. I mean if I had to rest in an airline seat for the rest of my life I wouldn't be happy. If Taki is on the smaller side it may not be an issue or it may be.
He's 5 months, 35 lbs after some food intolerance problems we've finally ironed out (he's now gaining), and… probably closer to 16"-18" at the shoulder. He won't hold still for me to correctly measure him. He'll be towards 65-70 lbs fully grown.
When you were watching her with the plastic, how long did she try to chew it? Was it test nibbles or the "hey this is kinda fun… let's eat it!" chewing? Have you also tried spraying it down with apple bitters? Sounds like you're doing fantastic with the exercise regimen. Do you play any "thinking" games with her? I know I see a difference in the crate if I play any game where my guy has to think and learn.
And don't feel too bad about the vet; my vet's staff know my voice with how many times I call them. It's usually with a "what do I do if my dog swallowed a lysol wipe?" or "so how big is too big again?" question. Once he even swallowed a glove the vet tech left lying around when he was back there getting weighed. Boy were they sheepish when they had to explain what happened and why he was drugged up. Another DS owner I know has some pretty funny stories about what his has swallowed too.
Facebook page.
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I just want her up off the plastic tray but will defer if the risk factor is that high. I don't want the fur worn off her joints from laying on a hard surface. She runs with me at least 3-5 miles a day, on grass, so I want a soft area for her to lay relative to a hard tray.
She was 42 lbs when we got her and in two weeks she had gained 5 lbs and then got the cow pies...so she won't be crated until I get this to clear up. The new vet I have is awesome and the Endsorb/Fast Balance/Flagyl treatment is working wonders! 
