What is your budget top?
The smallest I can remeber (apart from the DQG), is the Folomov EDC C4 (± USD$50)
You also have the On The Road M6, similar to the Olight, but less expensive!
It doesn’t appear that the clip is reversible on the BLF A6.
As to my budget, I’d like to stay under $30.
The On The Road M6 looks like a real possibility.
I also remembered the Convoy S9. It seems smaller than the S2 (can’t say accuratelly, though).
And definitely under 30 
I don’t have any experience with this form factor, but since OP liked the olight that much, isn’t replacing it with the same/equivalent model an option?
Well, the original model has been discontinued. I purchased it long before I found my way to the Budget Light Forum. Paid full price……I dunno, $45 or $50 dollars for it. Just trying to do better these days.
I’d say the On The Road M6 or the Convoy S9 (it is indeed a bit shorter than the S2+). Both come in various led tints. I like that the S9 has USB-charging.
I gotta say the On The Road M6 is the spitting image of my deceased Olight—right down to the magnetic tail cap. Looks like they came off the same assembly line.
A little OT, but does an 18350/short tube exist for OTR M6?
I think any 18650 light is going to be pretty heavy to put on a hat. Maybe consider AAA?
Not at all if you have the right light. I can keep my little Olight on my cap for two hours working on equipment in the dark and I’ll forget its there until I lift my head and inadvertently blind one of my co-workers.
Here’s a pro tip - drop Olight a line in Atlanta (the ‘contact us’ thingy is on their website); I’ve found them to be amazingly accommodating on warranty. Unless you ran over it with a D6 Cat, there’s a good chance they’ll give it an overhaul and send it back as good as new.
When I had a problem, I literally had an email response within the hour. I was very impressed with them.
I highly recommend the Utorch Ut-01. with a 14500 battery, it’s around 800 lumens and will run on AA batteries at around 400 lumens. With a coupon code you can get it for $10!
Second, if you wanted an 18650 light, the Jetbeam E40 is pretty small and light. It’s 1100 lumens and cost with a code is $36.
Yup, that is the smallest/shortest 18650 light I know, and even then, while I did use to walk with it attached to the brim of my hat, you can definitely feel its weight, which makes it problematic.
Nowadays I walk around with either UT-01 or OTR M3.
Why don’t you fix your light?
Replace the driver and emitter?
If there may come a time I can’t order a new Convoy S2+ I’l fix it :).
Astrolux E02 should do you good. $21.53 at FastTech.
https://www.fasttech.com/product/7028901-astrolux-e02-led-flashlight
The lightest 18650 light that I own is skillhunt h03 (angle light).
No chance of talking you into an actual headlight? Not to crow about it again, but the RJ02 is dirt-cheap, you can replace the TIRs from spotlight to wide-angle in a minute or less, and it gets pretty good runtime.
With a 60° TIR, it’s perfect for me, nice’n’floody.
Plus, you can swivel it up/down with those nice rubbery rings (ie, no discrete hinge that can break oh so easily) so you don’t have to constantly crane your head in the preferred direction.
Just today a thread has started about a new light that fits your requirement, the Ultratac S20
The way the clip is placed, when you reverse it, I think it will make it difficult to carry on the brim of a hat. It will be sticking pretty far out, thus making its weight more noticeable.