It can be done and without sealant...Here's own similar non-leaking, single inner o-ring Igloo:
I think I've identified the kit as this:
https://www.ontariobeerkegs.com/weldless-mash-king-bazooka-kit.html which is the current version with o-rings that replaced the eternally headachey flat washer version. Here it is:
Assembled thusly (as the OP has done):
It
does not use a coupler, but a short 1-1/2" nipple...the central ring is small enough, that between the cooler walls and outer washer, it allows the o-ring to be tightened over it making excess teflon tape unnecessary; the inner o-ring will have smooth contact.
The First Rule of building your own gear is: Always Buy Extra Parts! Particularly; nuts, washers, o-rings, various sizes of couplers. Without resorting to a pipe wrench, if you have 2 spare locknuts here's how you begin:
Wrap your few turns of tape on the inside, then turn the o-ring and grooved locknut(1)
all the way to the middle so the o-ring is wrapped over the smooth ring. Turn nut 2 most
but not all the way on. Turn and tighten nut 3 against nut 2..very tight and then with a wrench on nut 3; tighten nut 1 till it won't go any further, then with a pipe-wrench, tighten the coupler against it while still holding with a wrench on nut 3. Now that the inside bits are as far on as they go and the coupler is tightened against it; put your wrench on nut 2 and turn nut 3 off and then you can remove nut 2 by hand, wrap the outer part with tape, insert into the cooler, put your big washer on and then get your ball-valve as far on by hand as you can and then tighten it by holding the
coupler on the inside with a pipe wrench and turning the whole ball-valve and
not the inner coupler.
You're not likely to get the ball-valve in the proper upright position on the first try, so don't torque it all the way until you've rotated it enough by trial and error..You can back it off a bit to rotate, and I should have mentioned above: Put a bit of keg lube on the o-ring anyway. Getting threaded fittings such as a valve oriented in the correct position is one of those things you 'get a feel for' with practice and with the plastic cooler walls, the final position can be a bit tricky to hit...If I remember mine correctly; I hand tightened the ball valve as much as I could and when I finally got the right position, it required about 180° turn with a wrench to get the handle at the top and be fully torqued.
Hope this is helpful.

EDIT: I forgot to mention: I didn't have a 1-1/2" nipple on hand, (But that is what is inside my own Igloo MT) I used a 2" coupler just for the pictures, yours will be shorter than seen here.
Also: If you don't have a couple spare nuts, you can use a pipe-wrench..but be very careful as that can damage the threads, hence the preferance for 'nut-on-nut'.