In most circumstances, I agree with your first point, meaning if you can only reach diamond, diamond 1 is the best league to be in at the end of the season.
But if you can reach champ, you should go for that, in my opinion, even if it's only CL3. Champ chests are much better than diamond chests. Matt commented in a Splinterlands show that they might need to make champ chest less rewarding if the difference compared to diamond is so high.
On the second point, even if you remain in the same league and don't advance, and don't deplete your ECR more than necessary, it's still worth playing during the first days. You still earn SP and FP. I earned 8 champ chests in almost two days in gold only from season rewards, plus 2 focus chests, while making enough mistakes. One of the champ chests gave me over 3000 DEC.
One other piece of advice would be to not target the focus mission, especially in the first part of the season when you aren't high enough, and to not use the same splinter continuously, especially if you don't have different developed summoners. Just advance to the higher league first (i.e. from gold to diamond), regardless of what you play.
I finished in Champion 3 and then at the beginning of the season I droped into gold 1. In my FP with about 10 games won, I only got 1 single chest. Well it was a good chest because I got 24K DEC in it lol.
It's maybe too early do draw conclusions but I think we will only see at the end of the season how things are going. If I manage to get to champion a couple of days before the end, then I will definitely be able to get some chests :-).
You are right to point out that playing too much focus missions can be bad. I believe it makes sense to ignore them and climb the leauges and then concentrate on focus missions in the second half of the season.