Are you sure you need Tor for all youtube videos? If you only need youtube access, then you should try alternative lower latency circumvention techniques, like alternative DNS providers or a VPN. Tor should be used when you're worried about your government even knowing what you watch, meaning countries like Iran, China, Syria, etc.
Case 1. You care about speed and access, but not really privacy.
You should first try bypassing your nation's DNS servers by simply setting a DNS server outside the country. OpenNIC and OpenDNS are cool, albeit maybe slow. Google has some faster ones. etc. All these options worked fine in Turkey.
If your country blocks more than DNS then try using a VPN based outside your country, including free ones like VPNReactor. VPNs are slower than simply bypassing a DNS block, but almost any VPN should be faster than Tor. Or even a dedicated youtube proxy.
Case 2. You care about privacy more than speed.
Use Tor, preferably Tor everything mode. There are security risks with using youtube's flash app through Tor, probably this specific issue doesn't impact youtube's android app. Yet, maybe Tor's "select apps" mode doesn't adequately handle the NDK, where youtube's codecs probably live. If so, that's harder. Try a browser maybe?