Well, 3-4k$ can be small or a lot. Even higher budgets have to be very carefully managed otherwise we would risk that people join just for the prizes.
I suggest you to get a look at the Publish0x way of acting in the Contests. Here is one of the last I took part to. Publish0x has these stats https://www.publish0x.com/stats
With 1200$ of budget per contest, there were tens of posts submissions with consequent shares on social profiles.
We can start with the first one about why writers joined the Hive-chain AND why they would suggest people to join it.
To take part into one contest I once submitted also a song, winning the prize for the most original submission that create a huge hilarity.
About Youtubers, I see your point. Having them involved would be the best solution because they can tell the story but showing results and proofs would be the best solution. So I think it can be a matter of involving ONE youtuber that is monetizing his/her channel, telling "hey, do you know that Hive can make you monetize much better and more easily your contents?". He/She starts for some time and once he/she starts publishing results, others will follow because youtubers are growing in number and many of them are starving