HI recDNA, so the search goes on it seems.
I limited my initial recommendations to AAA/USB lights but since you seem open to suggestions, another pocket thrower that I rotate EDC is a DQG AA-slim.
It's an odd duck, actually uses a ½-AA (primary OR rechargeable) lithium, which is smaller than even a CR2 and it uses an optic for throw. There is also an extension tube (sold separately) that will allow the light to be used with std AA as well as 14500 cells. Even in full AA format It's about as small as an AA light can get. I carry it over my NC TIP when I think I might need throw over wide. Note though that it only comes in SS, Brass or Ti so there's slightly more weight compared to Al.
I don't have the NC EZ-CR2 but I do have an EZ-AA which might work for beam comparison. Here are some photos for your reference, taken with cellphone at 3- ft from wall for hot-spot comparison.
From left to right order - Nitecore TIP (it's there, just no hotspot), DQG Slim AA, PK PL2, EZ-AA (3-ft from wall)
The latter three lights without the TIP, which as you've discovered is so floody by comparison that the hotspot doesn't even show.
(from Left to Right) Slim AA, PK PL2, EZ-AA
All were set on their max level. The PK PL2 is tighter than the DQG Slim AA (almost as tight as the EZ-AA) but the DQG Slim AA is 2x brighter which will help with throw.
Happy hunting.