Is there any way to increase the YouTube API v3 Quota Limits?

Yes, there is an elaborate form for applying for higher quota.

It is linked in the developer console for example at: http://console.developers.google.com/apis/api/youtube-json.googleapis.com/quotas?project=YOURPROJECTID

The form starts off with some statements:

This Application will ask you detailed questions about:

(i) your business, (ii) your use of each YouTube API (current and proposed use, as applicable), and (iii) each of your website or software application that uses or will use YouTube API(s) (each an “API Client”).

This application also requires you to submit screenshots and design documents relating to your API Client(s) and your use of YouTube API(s). If you do not have these ready, please apply once these are available.

We will strive to respond to your application as soon as possible, provided that, all required supporting materials are submitted and sufficient, and all questions are thoroughly answered.

Note: Please do not apply for more quota unless you are actually close to hitting your current limit.