First and foremost, congratulations on your weight loss!
IMO it would be more important to focus on just building your physique, packing on smart mass and getting into the lifestyle rather than focusing on numbers or scale weight and body fat. To be honest your goal is not realistic. If you're 160lbs at 17% body fat, then to be 180lbs at 10% means you're walking around in the offseason 50-60 lbs heavier than you are now! Don't focus on numbers, just focus on your physique.
Cutting to 10% is damn tough to do honestly, the amount of LBM you can build on a cut is limited, especially the harder you're cutting. I think the best course of action would be to get on a good training program, learn how to eat properly at maintenance to build muscle and not put on excess fat, get some recomposition going, and after you've packed on more LBM, worry about cutting. If you're 5'9" at 160lbs, you've got a lot of muscle to add.
Just my thoughts, if you want to really develop your physique, a full body routine is always a good way to go. However, if you're only in the gym 3 days a week, that lowers the TDEE, ultimately lowering the amount of food you can eat to grow. There's a big misconception out there that only steroid using bodybuilding should be using split routines, and that's not true. A good PPL rotation, or classic bodybuilding split, would be a great program, give lots of frequency in the gym, up the TDEE and allow you to eat more. You won't get fat as long as your nutrition is in check, and I bet you'll notice some incredible growth with consistency.
Regarding cardio, if you're trying to gain muscle ideally you wouldn't be doing any, any would manage your caloric intake through nutrition. That being said, there's nothing wrong with a couple of brief LISS sessions throughout the week. However, 2-3 hours a week, I'd drop that for sure. Additionally if you've been doing cardio for along time, your body has adapted to it and you'd need to do even MORE to get the same results. I'd recommend a solid break from cardio, focus on training and nutrition.