The minimum amount of data needed to verify blocks and transactions is the UTXO set. The thread linked in the OP is a discussion about the best data structure for storing the UTXO set, with the goal of eventually including it into the block definition. If this is accomplished nodes could discard all prunable data, except for enough recent history to handle reorgs, but could still perform the network functions a reference node can perform now (except a full blockchain download).
All you've done in the second paragraph is describe how the Bitcoin-Qt app currently works. If you're maintaining a full copy of the UTXO set and verifying signatures, etc, then you're a full node by definition because you aren't relying on the majority consensus for anything except ordering.
It isn't feasible to do this in the places lightweight clients are currently used. It doesn't make sense to run a full node on a phone, for example, and as traffic ramps up it'll stop making sense to do it on laptops as well.
This is why I don't understand the proposal. The only reasonable way I've seen to get something in between SPV and full mode is d'aniels suggestions for various kinds of fraud proofs, but the whole point of a fraud proof is that you get one when the best chain is no longer following the rules .... making fraud proofs that rely on trusted commitments to the state of the UTXO set pointless (they would be a part of the fraud).