Love those Lian li cases.
I think the A04 is one of the better old ones.
I would hate to discard it.
I really think you can get it to work, and well.
What is your current cooler?
The 7600K does not come with a stock cooler.
First of all, two front 120mm intakes should be sufficient.
You can increase the intake capability by using higher rpm fans if you really need to(at the cost of more noise)
Your R9-280x is a very hot graphics card and needs all the cooling air it can get.
If you use the front intakes for a cpu cooler radiator, the motherboard and graphics card is going to have to work with heat from the cpu.
With two front 120mm intakes, the air will exit SOMEWHERE, taking your cpu and gpu heat with it.
A single 80mm exit fan is good to direct the airflow to the rear and top openings.
Leave off the extra I/o expansion covers too, it can only help.
Your case is 177mm wide. Measure the height available for a cpu cooler.
Normally, 160mm buys you a top performing air cooler.
But, your space may be less.
One of the best with a 120mm fan is the cryorig H7.
https://www.newegg.com/Product/Product.aspx?Item=13C-000U-00005
You may want to orient it so that the heat is directed up towards the top 120mm opening instead of the traditional rear orientation.
You may not get the top possible cooling, but it should be better.
You may well run into your safe vcore oc limit before you run into heat limits.
FWIW:
As of 6/19/17
What percent of samples can get an overclock
at a vcore around 1.4v.
I5-7600K
4.9 72%
5.0 52%
5.1 27%
5.2 16%
5.3 samples exist, unknown % of occurrence
If the cryorig H7 is unavailable, or you do not have 145mm available, here is the noctua TDP guidelines.
Noctua is top quality and uses quiet fans.
https://noctua.at/en/tdp-guide
They offer detailed dimensions so you can check compatibility.
If you still want to pursue liquid cooling, look for a 120mm radiator unit.
You should be able to mount it in the top 120mm opening, drawing cooling air from inside the case.
If needed, some, or all of the radiator/fan can be mounted outside the case.
I would use a fan with a full 25mm depth instead of a weaker half height fan.