Nine inch width might make for a tight fit on a stock swing arm but your 3" should be fine. If not trim you side tread bars. You can always try trimming Russian style.
Reminds me of early days of Bighorn and Bighorn II ATV tire installations stimulating discussions for need of swingers extensions to gain width and length clearances. Did not Ronneydog have that size but in a Bighorn II?
A 3 inch extension will increase your suspension travel proportionally, say 7 inches just for discussion. Should bike have this 7 inches of clearance when swing arm is fully extended then no problem. Clearance might become issue with rear sub-fender/taillight assembly since tire is 3 inches to the rear and travels further in an upwards arc than stock.
I would suggest a 60 tooth rear sprocket for gearing compensation as well as to overcome all that rotational inertia from the tall, heavier tire.
Either way there should be a significant increase in flywheel/ gyroscope effect compared to stock and will really help maintaining momentum over rocky ledges, logs and other obstacles.