This is very nice! Personally I'd really like some kind of login for the uploader so I can offer this service to friends and family (and myself ;)) without the risk of someone discovering the url and using it as a way to distribute illegal things... Perhaps it is easy to do with Apache/Nginx (when the upload site is on another subdomain for example), I don't know actually.
The speeds issue can be solved by running on a cheap DO droplet or scaleway arm server btw (my city luckily has fiber everywhere :)).
You could opt for the S3 storage provider, which will dump the files to Amazon AWS instead.
The YouTransfer project does not implement access control or SSL, so it is highly recommended that you look at the hosting options on the Wiki (https://github.com/remie/YouTransfer/wiki/hosting).
I'm afraid there is not much the project can do concerning upload speeds of individual connections at home :)