I think in some fashion you might like what we're doing for our 5E mod.
At level 0 (prologue) you will typically have only 6-10 HP (but ACs are better, so taking damage is a bit rarer). However, you have 3d8 for hit dice. So, you can spend 1d8 at a time to replenish some of your HP during the encounter or at any point during the day.
You can also withstand another 5 HP (potentially, depending on spend HD) before you actually die.
At level 1, you will gain about 5 HP and another HD.
It doesn't have as much front loaded HP as 4E from the sounds of it, but it is better than 5E at lower levels. However, since we don't add a HP bonus per level for CON, HP are lower at higher levels once the frontloading is "caught up to". So, eventually you will have smaller total HP, but you have a bit more HD for natural healing. It makes individual encounters more risky, but keeps over all survival pretty close to 5E.