I don't know all the details of the proposals, but let me explain it the way I see it and then you people tell me what I'm missing.
I propose "trust levels" as the name. For simplicity, I'm assuming the root of the UTXO tree is part of the headers, not just merged mined, but we can argue about that later.

Trust level 2: The current Simplified payment verification.

Trust level 1: We define a distance in blocks to the past which is secure for the node to assume won't suffer a reorg, say 1000 blocks ago and call it the "pseudo-checkpoint". He downloads the full UTXO tree that was in block (currentHeight-1000), the UTXO tree in the pseudo-checkpoint. He downloads 1000 blocks and reproduces the current UTXO tree from the the old one. For a given unspent output, he can provide its full merkle branch until coinbase OR the pseudo-checkpoint if the coinbase is older.

Trust level 0: The node downloads the rest of the chain, being able to verify that the UTXO tree from the pseudo-checkpoint he used was correct, and he will be able to always provide full output markle branches to their coinbases from now on.

You could download the whole chain from the top to the bottom and optimistically start assuming the last UTXO tree was legit, then validate it with the previous one and the transactions of last block, and so on to the genesis. Effectively decreasing the pseudo-checkpoint height from last block created to genesis.
Once you've achieved trust 0, nothing forces you to store the whole chain. You can then set another pseudo-checkpoint, only being afraid of reorgs and/or not being able to provide long enough output chains.
In fact, you can go to trust level 1 or even trust level 0 to operation level 2 if you want. You can download the whole chain but then only keep the branches of your own outputs.

Nodes would have more room for specialization. I think there will be always "librarian nodes" ala block explorer. distributing the whole history. But I think their lack is what worries @Sukrim.

After this I think you can only improve the storage of the UTXO (and posibly their full merkle brach) using caches.

Is this basically what we're talking about or am I lost and the name "trust levels" is awful?