Well, there are 2 parts to that question, I can certainly help with the 1st part
On the repository module, edit the form.html file for the template you are using, and change the [FILE] token to [URLCONTROLFILE] and change the [IMAGE] token to [URLCONTROLIMAGE]. That will tell the module to render the core URL control for uploading files and images. The core URL control allows you to upload a file to your server, or enter a URL to the file if it resides on another server.
As far as finding another host, there are plenty around and it mostly will depend on your budget and how much disk space you think you are going to use. I can't help your there. Personally, I use WebHost4Life.com. I have had no problems at all with them, although , as with most things, your mileage may vary. PowerDNN is generally regarded as one of the best for hosting DNN sites, and as expected will cost a little more than others.
Video is such an integral part of the internet these days, if your hosting provider won't let you upload video files, then I would stongly suggest getting another hosting provider rather than have to pay for 2 providers, one for hosting your web site, and one for hosting yoru files.