1st still dont understand why they call regular long road dropouts horizontal when the track dropouts are horizontal as well.
2nd... add 5 mm of washers at each side of the hub to make it up for the 10 mm in difference with the bike rear end (130)
3rd... go to the lbs and ask the guys for BB shell spacers, grab one and put it between the hub and the cog (if you cant figure it out where to put then we a serious problem), that will bring the cog tiny out. Put the lock ring.
4th... that the lockring it tight doesnt mean the cog is, probably the cog is lose and u havent figure it out yet. Obviously if you have a fix gear you shouldnt have the problem you are having, besides the a lose cog i doubt you have more lose parts for that to happen.
5th... diamant is a well known brand between old people, is not obscure or anything. If unknown to you then thats another story
, they sponsored pro teams back in the day. Very good bikes so I advice you to take care of it because probably you wont see another one in a while. People doesnt know what they have sometimes.