I'm afraid offering $7500 on a $10,000 horse is going to seem like a slap in the face to the sellers no matter which way you slice it. It's a lowball offer for sure. I usually assume that the wiggle room on a horse with a "negotiable" price is usually about 10% of the asking price.
That being said $10,000 for a 17 year old is a LOT to ask for. Even with a show record and lots of experience, I would say they are overpricing the horse anyways and $7500 is probably about the right price for him. I actually think that might still be a bit much for him. At that point, you're paying for the word "warmblood" to be attached to him. Most horses have the ability to perform second level maneuvers with about that level of success, so keep that in mind. You're almost just as well to get a nice little qh or tb school master for half the price.
For instance: Flashy Chestnut 2nd Level Dressage
I don't know if this guy is anywhere near you but he's already schooling third level and he's only 14 for $8000. Far closer to your $7500 budget... Price Reduced-12 Yr Tb Gelding
How about this boy? 12 year old beginner friendly with show experience. $2000. Probably not very fancy but likely more than enough for you to keep learning on and you could easily get your $2000 back in a few years if you need to progress to a more advanced mount.
Anyways ... that doesn't really answer your question about negotiating tactics does it? I will stop rambling ...
Will you get a pre-purchase exam done?
In terms of negotiating, you're already breaking my first cardinal rule of thumb which is never go see a horse you aren't prepared to pay full price for if it comes to it.
The only thing for it now is offer cash and have someone with a trailer on standby to come immediately if the seller agrees.
Keep in mind the seller may not be willing to wait for you to have a pre purchase exam done if he/she is taking 25% off the price for you. They may want you to take the horse as-is ... with a 17 year old horse, I'd be extremely wary of that situation. He may be sound now ... but you will be kicking yourself if he is lame in six months from ringbone that could've been caught on xrays ...