I've got no issue with you recommending an aio for the SG13 or you liking the SG13 because you've used it yourself, just don't try to make it out to be something that it isn't.
You can't just assume that everyone wants the same thing you want. You might like that case and if you want that case and want to overclock as well an aio is your only option, but neither of those are a given here.
If you aren't dead set on that case then you can't justify the aio.
If you want a carrying handle the case is right out.
If you don't want to overclock all the worrying about cooling is pointless.
If you want a SFF silent build I'd still go with an air cooler, but a different case.
If you don't want a silent build there's always the fun option of single tower cooler + >=3k rpm fan.
You've recommended a very specific build for a very specific set of requirements (yours) which are simply not given here.
On that note I'm still trying to find out what Domo actually wants. That's why I haven't posted anything more constructive or even a part list yet. He needs to make up his mind about the handle, size and overclocking first.