I use the snappy pipe plug sockets, but in a pinch you use what you have and in a situation like this you do what you have to.
Based on what you wrote I don't think a new 3/8" pipe plug bit is going to help you at all.
A 3/8 " drive extension should work fine as it is the same size as the Snap On 3/8" pipe plug part # PPM412A that you asked about.
Actually a 3/8" Snap On extension provides a bit tighter fit than the pipe plug bit.
I don't see how the friction ball could affect things at all if your using a regular extension .

Your not trying to use a wobble are you ?
In this situation it sounds like you have two problems .
One the plug is really rusted in there and two that your 3/8" drive extension was not the right size , probably due to the rusty plug as well.
Either the plug takes a different size bit (10 MM ?) or it has rusted away enough that it no longer fits the 3/8" or both.
By just getting a " bit " that actually fits the size of the plug you may be able to muscle it out.
The best solution would be to try to break the rust bond and then use a bit that fits.
Try this, heat the casting around the plug then let it cool or blast it with some aerokroil .
Then heat the plug good and HOT , let it cool or aerokroil it.
It may just come out if you have broken the rust bond.
Hitting it with a hammer may help as well.
If it is hard to get to put the extension in the hole and pound on that.
Since the plug is that badly mangled/rusted inside that the 3/8" drive extension turns, you need a larger "bit" driver to remove it.
A 3/8" extension is around a 1/2" on the diagonal so the plug must be reamed out pretty good to allow it to turn.
A 10 MM is just a little bit larger than the 3/8" but that may be too small to work then there is a 1/2" but that is going to be too big and you could just use a 1/2" extension anyway.
See the links below for these.
http://buy1.snapon.com/catalog/item...d=1555&supersede=&store=snapon-store&tool=all
http://buy1.snapon.com/catalog/item...id=367&supersede=&store=snapon-store&tool=all
For a one time home use the cheapest and quickest way would probably be to sacrifice a cheap Taiwan or China short extension.
Find a 1/2" one and grind it down evenly until it just fits the opening and pound it in there.
If you have an impact use it back and forth in short bursts, tightening then loosening it until it breaks loose and comes out.
These plugs are usually not that hard to remove.
Once you heat it good, and get a bit that doesn't slip in it ,it should come out.
Good luck.