My first solution is simple: Make level 3 content also have a negative JC profit, just like level 4 content. That way the lower level content, the monthly events and the approvals act as a way to put JC into the economy and the higher level content removes the JC. By adding it to level 3 content it means that it's not easy to skip the JC sink, like how right now you can choose to not play the level 4 content and still have a reasonable competitive team.
My second solution is adding new ways to spend JC at massive prices - the idea is that, for the players interested in these rewards they'd keep reffing content and keeping the queues moving even if they don't need the JC for content because they're saving up for these rewards. And when they do get the reward they'd be back to low JC, making them ref for JC to play, preventing them from stalling at the top. It also solves the problem of stockpilled JC - if we add several 100, 200 and/or 300 JC cost rewards all at once the people with hundreds of JC can spend them on these rewards and go back to normal levels.
Notably, these rewards
cannot be something obtainable other ways, specially if that other way involves spending JC - if the rewards were the EXP records, for example, why would they spend a ton of JC to get a few EXP records when they can spend that JC playing instead and get the EXP that way?
(Yes, I am aware of it being more convenient, but the theoretical basis here relies that "playing the game" be treated as an inherently pleasurable and desirable thing to do - unpacking that besides that would be much, MUCH bigger of a talk and go on a ton of other stuff not really related to JC economy and the queues. For other reasons why this doesn't work, see the top of this post.)
If we go back to the example of Player A and Player B and Hop, imagine we add a shop that sells a desirable thing at 300 JC, and player A decides to save up the excess JC to buy the desirable thing, it means the queue would only stall after Player A saves up 300 JC rather than at 10, because they would still be reffing Player B's queue even if they're both above 10 JC (where they wouldn't need to ref in order to play) due to Player A grinding for the 300 JC item.
WHAT I'D SELL (Skippable section)
For 1 and 2, they're more so cosmetic/social purchases, purchases that are cool but don't inpact gameplay. They are the more expensive of these shop suggestions - 300, 500, etc.
1: A hall of fame. Make a hall of fame for top contributors, and make it cost ~300 / 500 JC. You buy it and you get put on it, alongside how many times you've bought it. Getting social recognition and status is something human beings adore, so I don't need to dwell much on why this would be desirable for people with tons of JC. I can even see non-approvers grinding JC to get here as a way of cementing their legacy on BBP.
2: Spiky-Eared Pichu. Heartgold & Soulsilver let you obtain this special Pichu that can't evolve and has a special ear; it's completely useless in battle, but it's a very neat collector's piece. It's a perfect candidate for what we want: Something inherently desirable but that doesn't affect the balance of the rest of the systems. I can see people with hoards of JC cashing some out for this for the novelty or for restricted pokémon collectors to grind JC to get this guy to their collection.
For 3 and 4, I'm pitching gameplay affecting game pieces. Stuff you can confortably or semi-confortably bring to a competitive match. These would be towards the cheaper end of things - 25 JC, 50 JC, etc. That way even competitive players would sometimes want to grind JC rather than always remain at that "enough to play" treshold, and it means if the queue stalled but they have enough JC to go by they have an incentive to move the queue along - not only does their game come by faster, but they also get spare JC to save for these items and rewards!
3: Restricted pokemon. This can be any singular or group of pokémon that aren't yet available - Shaymin, the Legendary Beasts, the Swords of Justice, it doesn't matter much which ones. I'm really not in the spot to talk about which ones would be of the desired power level so I'm not gonna speculate further; these would be towards the higher end of the JC cost. Essentially making it like the boasting hall or league circuit, where a few otherwise unobtainable pokémon can be obtained if you show extra effort for it. I particularly like the idea of putting Shaymin here due to it being the gratitude pokémon, but that's beside the point.
3.5: Non-adoptable Signature Held Item. You can put in Shaymin's Gracidea here I have realized that Shaymin-Sky is a fucking monster and might break the game in half. I am keeping this here for posteriority but this thing is crazy. If something here would have the 100 JC tag it would be this.
4: A few generic items you can only obtain here. Collecting items is cool, and having more ways of getting them than just the shop is cool. These would be the cheapest, at like 20 JC a pop so players can splurge on them if they feel like it rather than actively grind for like the other ones. They'd be balanced just like the other regular items like Life Orb, Utility Umbrella, etc, only with a different way of obtaining them. There's quite a few event-exclusive items that could fit: the Mythical Pecha Berry, the Enigma Stone, the Discount Coupon, etc.