Wool area rug help

I have a new 8’x10’ wool area rug. Used my Shark to vacuum it for the first time and quickly realized it needed special treatment - it lifted off a ton of wool and quickly clogged the machine. Not good for the rug or the machine. So, having never had a canister vac before I am looking at those. Here are the considerations:
I have LVP floors so not worried about hardwood issues. Also have other area rugs. Would really like to keep it in the $300 - $400 range maybe $500. 2 large non-shedding dogs who track in dusty dirt through the doggie door.

Would a Miele C1 do the job?
I’d pay more for the Sebo Balance A1 cordless because I’m used to upright and the cordless feature really appeals.

I am really stuck in this rabbit hole. Thanks!!

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u/phazer08 — 1 day ago

Previous owners (a couple of owners back) added the 2nd story to this house and did a really bad job. Apparently didn't get a permit and there are code issues. The stairs are narrow and steep so you can't get much furniture up to it. The porch is already rotting. I'm 67F widow and I'm never going to utilize it. I want it gone. Using my Photoshop skills and some AI, I've removed it. And the porch on the right is dark, dismal and the concrete slopes. So I've removed it (though if I can afford it, I might make it a room). And I've removed the pergola just to be able to visualize better. I love a contemporary look with cedar planks. I love red front doors or at least a complementary color. Help?

EDIT TO ADDRESS COMMENTS: Thanks for the suggestions and renderings and advice. You’ve given me much to think about. I will tone down my expectations. The house is what it is and I’ll try and keep the changes subtle.

u/phazer08 — 2 months ago