I just had a couple other thoughts on covering server expenses to allow uploads.
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You could publish server maintenance costs, and solicit donations and/or "memberships" that give priority access to available bandwidth. Sharing your actual costs and revenues from the above would help prevent fears of unreasonable profit-taking abuse among users. Any excess profits could be placed in an interest-bearing account to generate more funds to support activities, and act as a "slush fund" for future upgrades, repairs/replacements of hardware, and/or to cover periods where funding shortfalls occur due to things like a souring economy.
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You could give users the option of viewing ads to earn credits towards hosting their videos. Again, many people won't like this, but costs are a reality they can't really argue, and making this just an optional method of support means they simply don't have to use it if they don't want to. Finding an advertising company willing to do such small-scale non-targeted advertising while still sharing some of the revenue for it is admittedly probably going to be difficult, however. I think starting by looking at who the smaller-scale search engines such as Qwant and StartPage work with might be useful here. Overall, this approach honestly isn't likely to generate much revenue (at least initially) so it may not be worth the effort, but I don't know enough to say for sure - it's just an avenue to consider that might work better if & when you achieve some significant growth.