I looked at GBT, and I don't see it improving anything. It requires sending the entire block template (potentially up to 1 MB) to miners every 10 seconds, which is definitely impractical for remote miners. An extension to GBT that allowed only sending the merkle root would avoid this, though.
Yes we're debating that very point at length in the GBT thread at the moment, as I do not see the advantage of that either, only potential disadvantage of increasing network bandwidth, or worse, encouraging not perpetuating transactions. Stratum on the other hand uses merkle branches to negate this effect entirely and the bandwidth is
virtually static regardless of the miner's hashrate or transaction count.