You didn't understand since you think those 14000 points should remain in place. In my system, those will be reset for everyone. It is needed whatever the chosen solution.
Then after the reset, we reattribute points based on the rules explained, including past performance. So that it'll give a brand new ranking toping still around 14000 points. But most likely it would start with top ranked being around 11000 points at first. The thing is 1000 of those 14000 points are "volatile" depending on current and average performance while 13000 are for solo and best performance attained.
The system ensures that good performer can attain the 13000-14000 range and that the system doesn't hold the first spots for people who made all the previous challenges including the ones with very few contenders that were more easy to win than actual ones but still grant a meaningless amount of points today.
Your questions :
"if I'm ranking X in this contest, what can I expect for my global ranking?"
=> You can't expect anything precise in terms of ranking since a ranking is not based on your sole performance, but a combination of everyone's performance. Thus, you are wrong thinking you should expect anything precise. At least in my system you know what to expect a little : the possibility to raise you max global ranking for this kind of trial, the possibility to raise your max language ranking for this kind of trial, the possibility to raise your average performance for this kind of trail and the certitude to get 0-200 points instead of a plain reset to 0 for the "latest trial score".
"if I'm ranking better than this person in this contest, can I now be in front of him in the global ranking?"
Of course not, a global ranking, as stated by its name, includes all factors, not just this trial ranking one. You had the answer in your own question.
"These are the kind of questions you probably won't be able to answer thus it'll likely kills part of your motivation if you're interested in global ranking."
Wrong, the system I offer ensures at fierce and permanent battle for the top since you can't just sit on your old contests performances (which is clearly the case today, since any newcomer can't get past 5000 points which means ranked 150 tops).
"Moreover, you can't free the top ranks with a max loss of 400, knowing the maximum is 14000 (at the moment) because that's less than 3%. So the leaderboard top could be bloated with people who aren't participating
anymore in any contest."
With my system the max loss is 1000 which is plenty enough room to make it a fair battle. Also my system doesn't take into consideration the number of attended battles (just the average), which is fair in more than one way. First your skills evolve, second it would be unfair to newComers. Also, the points stated in my idead could be adjusted to enhance to 1000 volatile points. But I think it's enough. Someone being first at a solo and a multi contest who solved all solo games and went 1st in all multi once, but who stop playing could get 13000 out of 14000 points. I think it's kind of normal at least. Getting him very much lower, wouldn't be fair performance wise.
"And finally, though people should be able to quickly reach the leaderboard top, you can't let them do it with only 1
solo contest and 1 multiplayer contest because that's clearly not enough for a meaningful ranking."
Again it's not the case, 1 contest of each (even ranked 1st global) would give 6000 then 5600 points 2 months later if he doesn't participate in the next challenges. To reach the top he would need to completed all solo games for 5000 more points approx and get ranked 1st in all 6 multi games for 3000 more. If he does he would approach the top. Don't you it's pretty normal after such a performance?
Also I guess no one ever ranked first in all multi challenges so the points would be much more distributed.
Doesn't the system do the intended job?
As a self criticism, I think the live performance points (current IA rankings) should be calculated based on ranks every hour/half-day/day or so because live computations would probably be a little overkill cpu wise.