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Frame alone is 1.75kg for a 54cm. How do you mean strictly track designed? The alpina forks you can get with it are not all drilled for a front brake but I have some drilled forks already. Not sure of the weight of these but there are affordable alternatives from chinese eBay that would bring the frameset to just over 2kgs.
Is a frameset that weight unrealistic for a <7 fixed?
Arnomatic-
It's just the weight of a bike doesn't really matter much on track, therefore track bikes are made heavy but stiff. Heavy is the opposite direction this project was supposed to go, nah?
EDIT: If focused on the weight you can always try to go for a road alloy/carbon frame and have little bit fun with halflinks and fitting right cogs, chainrings. That would be the easiest gain on weight not being spendy at all.
ShutUpNoRest
Pre Cursa is fucktone heavy as it's strictly track designed bike, no? I remember having PC fixie, brakeless, crabon SP, crabon forks, flite Ti and rest of the parts being just random secondhand semi-decent trash and it all weight quite much more than my friend's roadie.
EDIT: I just remember now, budget for whole project was much under 300quid, so maybe it's possible to make it lighter.