boris, I wouldn't be too concerned about the low FG. A fast ferment of low- mashed wort can leave it tasting a bit ordinary and low on the good flavours we want, but should still be still excellent comparatively speaking. Often my low- mashed UK Bitters get to 1.008 and lower with high attenuators like 1469, but don't lack at all for character, I'm after a quite dry beer.
No worries keifer, I do that overnight cooling all the time, makes for a simple process, shorter brewday(s) and no extra equipment (chiller etc) plus I get the 'free' warm water to clean up with! I've also poured from the kettle into a No- Chill cube through a sieve in a big funnel, but it isn't for the feint of heart, syphoning is probably better (no HSA problems either). I'd just be wary if you're leaving it to cool un- assisted, I've not done that in- situ and if the temperature doesn't get down low enough quick enough then it may increase the bittering and offset the late additions, but seeing as No- Chill works then it should be OK. The other concern some might have is the break material, but I think we've worked out that the impact is probably minimal. If you can though, I'd recommend to pop it into the laundry/ bath tub for cooling, but it is up to you and worthwhile to try in- situ if that suits.