Try Goo-Gone--the oily stuff that smells like oranges. I'd test it first in an inconspicuous place to make sure it doesn't harm the finish. De-Solv-It is another brand. Good stuff, both of them. Here is a link that might be useful: De-Solv-It

This is an old post but for anyone who is wondering...the rugs that the designer quoted OP for are hand knotted and Nourison ones OP posted are hand tufted. Knotted is of significantly better quality and more luxurious than the Nourison tufted rugs. $25K for two is steep but that is because OP went to a high end furniture store. Furniture stores ALWAYS charge double because they buy from factory direct stores like RugKnots so they have to mark the rugs up to turn a profit. Factory direct will always be cheaper and of the same quality. The hand tufted rugs OP choose are wonderful but they do not even begin to compare in quality to a hand knotted rug. Hand made, hand woven, hand spun= Tufted by machine. The reason marketers get away with it because human hands load the yarn into the machine that makes the rug. They are NOT made by hand.

Try an on line room planner and include all structural components/measurements of room. The sectional can only go along wall with door & back wall, so that's a start. Then also test a couch/chairs, end table vs floor lamp, etc. Look on line for rooms that appeal to you and since you like navy start there. The first decision is the seating plus a style and the rest will be much easier.

something like this for living area then pull the blue or green from it for the dining area horchow.com $700 9x12 Simplify the TV area. I would not put anything on top of the entertainment center. Paint the vents the wall color