Infinity and Nissan, the same company as you know, have slipped dramatically in the reliability department, they are now rated in the lower 25 percentile of all cars made, this all started back in 2010.
I seriously doubt that one prolonged oil change caused sludge. What happened is the poor design of the direct injection system. Direct injection engines, fuel is injected directly into the combustion chamber under high pressure, which can cause carbon buildup. This can mix with oil to create a sludge-like substance that can clog oil passages and reduce lubrication. In doing so it will give your engine a shorter life than what you would expect out of it. And the knocking noises you might be hearing, I say might be hearing because I’m not there to hear it, but that noise is from the sludge build up.
Unfortunately here is the bad news. That knocking sound means it’s too late, the engine is basically toast, it doesn’t have long to go and then you’ll need a new engine at a cost of around $10,000 to $12,000 with a one year warranty, or you could find a used one, but there’s no guarantee that a used one isn’t already sludged up, but the companies that sell used engines are suppose to check them thoroughly before selling them, and they should come with a one year warranty, but that used engine with labor will be around $5,000 to $6,000 dollars.
The other issue with those SUVs is the transmission, at a cost of around $4,000, and the transfer case, which is around $6,000, they were not known to last long, so you could be replacing an engine this year, and the next the transmission! The total of the engine, transmission, and transfer case you could find a really nice used car!
I suggest you cut your loses and soon, and don’t buy any Nissan product, stick with companies that have a known track record for dependability, if you want another luxury SUV get the Lexus, or the Acura, but the Lexus is a better vehicle as far as build quality, reliability wise they’re close. If you want to save some money buy a Toyota SUV, they’re better than the Honda SUV. The other brand that is doing well is Mazda, but that one would be my third pick.
Buy a car that has very low miles on it, that is at least 5 years old, the internet has several car sites that you dictate the mileage and the age. For example, I bought about 4 months ago a 2002 Lexus SC430 with just 34,000 miles, for less than $10,000, it was garaged kept, all maintenance records from a Lexus dealership showed it to have oil changes based on months since it wasn’t driven much in the way of miles, and the car runs fantastic, for some reason it gets better MPGs than the sticker says, about 4 mpg more.
If your patient person you will find a good deal for what you want. The car I bought was a my retirement fun car, took me about a year to find it, but I did the same thing about 5 years ago when I needed another pickup, after 4 months of looking a 2010 Toyota Tundra SR5 4x4 with the 5.7 flex fuel engine with just 87,000 miles came up on a labor day sale, no place came close to the price I got it for, I ran down as fast as I could before they even opened. Patience is the key. If you can wait for labor day, which is coming soon, be looking at the internet sites like a mad man, then rush down real early in the morning, take the day off from work if you have to, because other people are seeing those cars too. Labor day is Monday the 2nd.
When I search for cars I try to buy locally, but where I live prices are for some odd reason higher then they are just 150 miles away. I did get lucky with my Acura and my Toyota and found those locally, but the Lexus, being a difficult to find car, I had to travel 155 miles to see it.
I know if you work those internet sites correctly you will find a nice used car with low mileage. All my cars were bought from dealerships, not private parties, and I only service them at the corresponding dealerships in my town, I have great dealerships, but a dealership understands their make and models better than a independent mechanic, and in some cases, as you found out, the independents can’t fix it. In some cases the independents are not the cheapest, when I had my Acura TL timing belt replaced I got independent quotes between $1,300 to $2,200, the Acura dealer did it for $980 (those prices was just before the huge jump in inflation, now those prices have almost doubled). Also when it comes time to replace the plugs, the dealerships will charge you about $60 a plug, you can buy your own for around $15 and take the plugs to them to install, most dealers will use your plugs, but you have to check with the dealer. My Acura dealer, and my Toyota dealer had no problem using my plugs, but that saved me a lot of money when you consider 6 plugs for one and 8 for another!
Enough rambling, hope you find a vehicle both of you like.