I'd imagine if you were to keep your dice and stats between levels, it would need a different kind of progression altogether, and enemies would need to scale more to still make it challenging when you would keep pretty good dice and would keep improving them through each level.
An idea could be to not get any additional dice during each level like now, but instead either auto-receive more dice between certain levels, and/or having upgrade perks you could select between when advancing to a new level. Such perks might be adding one active dice, get a smattering of extra symbols on your current faces, get an upgrade for a certain kind of symbol, add debuff resistance, get a permanent free shield each round, get a bit of regeneration each round or something like that.