Yeah other option is have a condensed WBC tournament in the middle of the season for either one week or two. Kind of like what the NHL did with the Olympics.
Players and pitchers would be in game form unlike during spring training which is a plus. I guess some starters would still be limited in terms of innings or pitch counts, which I understand. But at least maybe a starting pitcher can go 5 innings. Create a pitch count/inning pitched threshold for a SP during the tournament.
Like you said, limit the amount of teams in the tournament to like 8 or 12 (USA, Japan, Korea, Venezuela, Cuba, Dominican Republic, Mexico, Puerto Rico) and have others qualify like Canada, Italy, Australia, Panama, Colombia etc. based on their rankings or previous finish.
The one or two week break I don't think will have a major effect on players/pitchers not playing in the tournament. Might be good for some players as its a time to rest and get healthy in the middle of the season. Players and arms can always go down to their teams ST facilities to work out and stay in shape if they want.
An obstacle would be the host cities/countries. Would have to be in North America or Latin American countries IMO if in the middle of the season. Would be tough to have MLB players travel overseas to Japan or Europe to play.