I don’t think that Uzbekistan will have a problem. In general the ratio between the number of visas issued and the number of NLs sent out (Visas/NLs – visas per NL) is roughly around 0.8 for Europe as a whole.
I remember reading some statistics sometime back which indicate that roughly around 20,000 DV visas are issued for Europe every year. I don’t remember where, but I remember that you commented on those statistics too, so it’ll not be difficult for you to find again! ;-)
Since roughly around 25,000 NLs were sent out for Europe last year, I came up with this figure (20,000/25,000 = 0.8)
So if things go along the way they normally do, 3100 NLs should lead to (3100*0.8 =) 2480 visas for Uzbekistan. It’ll probably be even be less than that because winners in Uzbekistan may find it more difficult than those elsewhere in Europe to satisfy the “public charge” test by showing money in the bank etc.
So it is unlikely that the number of Visas issued for Uzbekistan would come close to 3500 which is the maximum limit per country. Thus separate country restrictions will probably not be necessary!
ps- all calculations and figures are very rough as this is meant only to be a very rough projection.