I'll try to find somebody, but don't hold your breath. I'm from Finland but visit Estonia regularly.
In the meantime I can give you quick explanation on the bureaucratic side of wildlife management in Estonia. The land is divided into "hunting counties" (direct translation, in Estonian it's jahipiirkond) and government will give them to applicants for certain time (like 5y) to administer. Few counties are administered by government (at least RMK, the local Forestry Commission), in most it's a mix of government and private land. Most usual county holders are local hunting clubs.
For landowner, you have to specifically deny hunting on your land if you so wish. Otherwise it's used by the county holder, but 200m around points of residence are off limits unless specifically allowed by the resident. Theoretically hunters have obligation to reimburse wildlife damage to crops and forests, unless they can show to have taken reasonable measures to mitigate damage (also landowner has responsibilities). If you deny hunting, naturally this removes the possibility for reimbursement, how theoretical it might be.
If there are several applicants for a given county, it will be given to applicant that has most written contracts with landowners. Or actually the most hectares but you get the point.
Each year every county is assigned the minimum number of game to be shot. This will be mostly based on reported game numbers in the county (county holder will do the yearly report). Some game (large predators) have regional quotas, and they are maximum not minimum.
A hunter needs to have gone through hunter education (quite comprehensive) and pay yearly for the right to hunt (10 Euro). In order to shoot certain animals (roe and up) hunter needs to take shooting test every 2 years. There are two tests, one for static target and one for static/moving target (actually the static/moving test is split in two, one for rifle and one for shotgun). If you take the test only for static target, you cannot participate as shooter in driven events.
Firearm licenses are somewhat same as in UK, they're valid for 5 years, you can have firearm for certain activities (protection, hunting, sporting) and while licenses do not state quotas for ammunition, it's in the legislation (300rds per hunting firearm and 1000 per sporting firearm or something like that).