One of the funds you list is leveraged 3x. If the market drops 33% you're wiped out, get liquidated, and can never recover.
You've already made the assumption that you can detect the market bottom to select when to drop the $3K, which is ludicrous, and begs the question if you're know where the bottom is why not put the full $10K in then with maximum upward leverage.
I think your strategy is making the fallacy that past performance is a guarantee of future performance. Using specifically picked events (e.g. 33% decline) and then assuming that the event not happening in the past makes it impossible to happen in the future.
Also how does TQQQ work. I don't know and I am happy to admit that. But I assume they need to do re-balancing shenanigans to keep the leverage at 3x, they have to pay interest on the leveraged money, and so on. So it is possible that the market takes a milder dip than 33% but you get stung on TQQQ - maybe not a wipeout but severely down and takes years to get back to break-even. Would like to hear from someone with knowledge of this.
If you have a long term alpha strategy - one that can beat the market every time - and it is as simple as buying an off the shelf instrument and topping it up. I would be surprised.
You've already made the assumption that you can detect the market bottom to select when to drop the $3K, which is ludicrous, and begs the question if you're know where the bottom is why not put the full $10K in then with maximum upward leverage.