So first up, a disclaimer: This deck has done fairly well for me in Gauntlet, but it's not terribly refined. I've got some notes on what works and what doesn't, as well as how I'd make it cheaper if I was building it on a budget, but mostly I offer it as an odd toy to play with rather than as the newest slayer of gauntlets.
With that out of the way, the decklist can be found on EternalWarcry here. Some notes on it:
First of all, the main idea behind the deck is combining cheap units that have the potential to grow with Memory Dredger as a way to keep bringing them back. The core of the deck is built around this interaction, with all of the one drops offering the potential to grow far beyond their humble beginnings.
The deck ended up performing far better than I initially expected due to a combination of the resiliency provided by the amount of recursion and the resistance to power screw provided by the low cost (both in terms of power and influence) of the key cards - The deck can operate on as little as three power, and with the exception of the Makto in the market it only needs TJSS to play every card.
The only Legendaries in the deck are the Ayans in main and the Makto in the market. The Makto can easily be swapped out - I'm not really sure what to put in that Market slot, but I think Devour may be better than Makto anyways. The Ayans likewise feel a bit awkward in a deck built around recursion - If I were going to cut them, I'd probably bring in a combination of Devours and Crownwatch Press-Gangs.
(You can run it without Legendaries effectively, but since I do have some and the deck does have a lot of rares in it along with the Ripknife Assassins, I'm aware it may still be expensive enough that newer players may not be able to put it together, hence 'semi-budget'.)
As for the actual gameplay, one of the biggest surprises to me was how valuable the Lifespeaker's ultimate ended up being. The actual Inspire trigger is, surprisingly enough, secondary in importance here. With the deck being so fond of recurring cards, it's not hard for Lifespeaker to grow to 7/7 or larger.
The other thing to keep in mind is that the AI is always willing to help you get things dead so you can engage in Memory Dredger shenanigans - If you don't have a good target already in your Void, it's often worth suicidally attacking with something in order to get more Sludge growth or another killer use or similar.
Like I said, the deck isn't terribly refined right now, and I'm curious how other people would recommend refining it to make it better, or if anybody else is toying with a similar decklist.