Puschkin

Yeah, because we all know how well the OP listenes to others ;)

So, in other words, you only posted to advertise your own deck ...

https://magiccards.info/dk/en/43.html

Ha, no, I am casual all the way and just think infinite combos aren't casual material, so IF you are going infinte in casual, at least end it quickly (thus Comet Storm).
Of course you didn't demand my advice, but you made this deck public, which usually means you are inviting everyone for a discussion. I won't bother you anymore, though, don't worry.

But you don't run Fireball, you run Devil's Play, which is NOT able to kill the entire table at once! Furthermore, for the majority of the game you will not have your combo active, so the spell must also be useful without infinite mana. Your biggest problem, obviously, is to stay alive. Comet Storm can take out multiple creatures, Devil's Play can't. Moreover, it is an instant, which is incredibly useful when dealing with creatures!

Look, if you your goal is to play combo but also to try to somehow make it subpar, then it's impossible for me to make any suggestions because you are the only person that knows your personal level of "crappy enough so it's fun" combo.

You answered your question yourself. Infinite anything isn't fun. Toning it down with a slower combo isn't helping, it just means delaying the infinite combo. That gives the pponents a higher chance of winning of course but it doesn't make the game more interesting.
So, IF you are going infinite combo in casual anyway, I'd say get Pemmin's Aura so the game ends quick and you can start over, changing decks.

EDIT:
Oh and change Devil's Play to Comet Storm if you play multiplayer, so you can kill everybody/everything at once.

EDIT 2:
And if you really want to walk the line between "broken but not too broken" you could swap the Alchemist for Crab Umbra or Freed from the Real, both are better than Alchemist but worse than Pemmin's. But I'd still say either play the best combopart or don't at all.

Okay, first off, why would someone want to play an infinite anything deck in casual?

Secondly, Galvanic Alchemist is a pretty bad choice to combo with Axebane, it needs three mana to operate (which means you need 4 walls) and the combo is disrupted if either the wall or the Alchemist dies. There are many better options and I think of all of those, Pemmin's Aura is the best, by far. With that, you only need 2 walls to go off AND it protects the Guardian, giving it shroud when you need it!

So, if your opponent runs just a few creature removal spells, you can't win? You absolutely need a backup plan here.
Also, again, yet another deck that has a gazillion ways to deal with creatrue threats but zero to deal with anything else. I mean, your deck itself is an example that decks can have winconditions other than creatures ...

Isn't that a bit farfecthed? Adding another component to make a splash work?

But with Solemnity, they also never die in your upkeep. So, if your opponent isn't so kindly and kills it, you'll sit on a single one forever.

The anti-synergy is actually different. The tokens don't "simply die", they are exact copies including the vanishing part and they keep on duplicating with more upkeeps. The actual anti-synergy is that new tokens have summoning sickness, so you won't be able to attack with many of them. Maybe that's what you said, your wording is a bit icky :)
The solution is simple, though: Don't play more than one Haze! I wouldn't add a full playset anyway since Haze does nothing in it's own. IF you have Chronozoa and Paradox Haze in play, you are in a pretty good situation anyway, so drawing a second one isn't that big of a loss. But a single Haze speeds up the petri dish so much more than any other option you have. I'd say you can run 2 of them and the possible gains will be way higher than the very occasional game where you draw both and don't win anyway.

I was just happy that someone asked for a challenge, nobody did for almost a year.

Of course there are many MANY ways to play a deck like this. Brutal Expulsion is a super great card, Aura Shards would rock in this and indeed be better than Hull Breach. I just wanted to limit this to 3 colours because of your budget restrictions. This deck could run other colour combinations and look very differently, my first draft had white and black as well. Current deck has no lifegain, which is kindof problematic.
Repeal, Repulse and Annul, however, don't add much since they are mono-coloured.

Here is the deck:
http://www.mtgvault.com/puschkin/decks/occ-rainbowlobber/

Note that my version was explicitly budget. You can (and probably should) soup up the mana base a bit just to get sure you have the right coloured mana early on.

Yeah, as I said, the sideboard holds the cards for a less budget version and Isos are among them (when I built this deck so long ago, Isochron Scepter was 5 or more dollars).

Paradox Haze.

And Epochrasite looks like it would fit the petri dish theme as well as the mechanic wise.

deckdescriptions would help

Ah, yes! Enter the Dungeon aaaaand Grenzo!

Soldiers and Knights are the easiest part, though.