> 15.6mA - which is pretty close for the TLEActually, it is over the limit, since you need to dump current from both channels. As for the BUF634, you will find that it is a bit expensive and also seems out of stock at many places right now. Therefore, it is probably better to go with the opamp method. However, according to datasheets for the parts you have, their maximum output current is 35 resp. 40mA, which does not provide that much headroom either. On the other hand, they are dual parts and there is a way to parallel both halves.
If I was building virtual ground like that, I would probably go with OPA551 as it can give you up to 200mA. There is a downside, though, as it might like more voltage than single 9V battery (absolute minimum for it is stated as 8V, and batteries discharge...). In fact, I have built an amp like that - OPA551 in the virtual ground as well as in L/R channels (I had bunch of those opamps). Works just fine with Grado, but I didn't try to go that low with voltage, I was feeding it some 20V+.