Hi there, I must confess I think this kind of perma progression would be too much of a change from the original game concept. The idea is for this game to have the kind of replayability that comes from each run being different (different weapons, items and even different mobs will appear in a new run) and where the player is motivated by trying to get further, with a better build, than on previous runs and so get a new highscore. Permaprogression would make this kind of progress more or less automatic, and therefore remove the sense of challenge. Based on my own playtesting I know it is quite possible to beat the 15 levels of the Alpha 1 without just relying on good luck, so you should be able to get further each time by trying new tactics/strategies - but do let me know if you think this is not the case and the game is just too hard!
However there is another sort of permaprogression I am planning to add, namely Achievements (including on Steam) which naturally can be unlocked over multiple games, so hopefully this will also help give you a sense of increasing progress over time.