Perhaps we should have a look at speed skating

It's an individual sport, it has organized a European Championship since 1893, it has a number of countries that are traditionally dominant and that generally have faster skaters. Not so different from go, I'd say

One idea that could copied from speed skating is the idea to allow some countries more participants in the EC, based on some qualifying criteria. In speed skating, a country can have up to 4 representatives. Their criteria are based on a qualifying event. You're allowed:
- 2 representatives if your country had at least one skater finish in the top 20.
- 3 representatives if your country had at least two skaters finish in the top 16.
- 4 representatives if your country had at least three skaters finish in the top 12.
Countries choose their representatives themselves, but the ISU additionally requires that those representatives have shown sufficient performance (times they must have beaten) in the last year. The hosting country is always allowed field at least two representatives.
Such a system could also be applied to a European Championship, if it were to be separated from the EGC Main tournament.
With the criteria above, there is a good chance that strong countries would be able to send 3-4 representatives, while weaker countries would always be able to send at least one (unless you also copy the additional "performance" requirement, which could be something like "Achieved at least rating X in the past year").
You could also allow the local organizers to specify an additional reserve player who is allowed to play if the number of participants is odd.
The largest downside, IMO, is that this will result in a pretty large group of participants (could be around 50, I'd guess), so perhaps it would be suitable for accelerated pairings.
EDIT:
The ISU criteria for their World Sprint Championship are:
- Members without Skaters among the 28 best: 1 competitor;
- Members with at least 1 Skater among the 28 best: 2 competitors;
- Members with at least 2 Skaters among the 22 best: 3 competitors;
- Members with at least 3 Skaters among the 16 best: 4 competitors.