Although a lot of attention has been focussed on the room, what about the player? If we create a "small" isolated space, what happens to our sound? I can tell you, it becomes small and isolated too! The biggest problem for my best young students is practicing in their bedrooms.
I think we are dealing with several things here and unless the house has a VERY large room that can be treated (room in room), maybe the $3500 should be donated to a church for practice rights........
For $3500 you can build a room in a room however. Just make sure that your practice space is big enough. If the room is not square, play to the wall furthest away.
Here is one example near your price limit:
DIY: Build Your Own Soundproof Home Studio - DRUM! Magazine - Play Better Faster
The hardest part of isolation is ventilation. We need fresh air to practice near our potential............. Here is one solution for that.