That's a lot of money to throw at a car to maybe fix the problem. My impression is that your engine hasn't had much care over its life.
I would recommend getting either a gadget that plugs into the OBDII socket and gives you some actual data, such as the fuel trims and other readings OR a VCDS cable from Ross that will attach to a laptop and let you have more control over the engine management. I use this one for convenience:
Actron CP9600 U-SCAN OBD II and CAN Wireless Smartphone Interface
If the engine is indeed running lean then you can readily suspect an air leak somewhere. These can be easy to find or they can be hard. You can check every hose and connection yourself. If a vacuum hose looks the slightest bit cracked, replace it. Next, search for the location of your PCV valve and it's associated brittle plastic parts. If cracked, you can swap them out. If your gadget still shows a lean condition, then get the engine "smoked" by someone that has the knowledge to do it right. If the intake is leaking, the smoke will show you. All this that I have said so far should cost you about $100 and a little time.
Plugs and coils are well worth the cost on an engine with your miles. Fuel injectors? I would first change the fuel filter, then use good fuel injector cleaner in 2 consecutive full tanks of gas. I did that with my S4 and felt the difference immediately.
If you are sure the injector for cylinder 10 is bad, it's not too hard to swap out. In fact, you can pull all of them out, send them away to be rebuilt, and reinstall them. They cost about $12-$20 each to be rebuilt that way. Watch some youtube videos and see if you can do it.
Good luck, my friend!
2008 S4 Cabriolet 6-speed manual 1 of 2 in US