Ok, hottest of hot takes above from my first game of the update aside, I think I get what's going on with me being a bit averse to the frequency of the mini-games:
The main game is clearing customers by grinding cheese. The mini-games are distractions from this goal and feel like more of a threat than a treat. It's like that closing door psyche experiment, but in this case it's "deal with this game, or it will cost you". I call them distractions because they don't get me closer to ending the shift, I don't know how many are coming in a round as opposed to customers in a shift counting down, and they don't break my combo when I fail them. I don't mind the clown wheel or cheese lover games at all because that delay just me waiting on my guaranteed bonus reward beyond what I get for clearing the customer. Coming out of 2 mini-games and into a reload is jarring since the mini-games no longer deal with the cheese grinding so, I often forget that I might have been close to a reload. The grind only versions of the game make that rhythm easy to keep track of at the expense of variety. Maybe crazy, but could we see the cheese in the grinder go down visually somehow?
Also, my aversion to Cheese Greatest has been making the game way harder than it needed to be since I'm playing on default crank sensitivity. Because my cheese dispensing was so slow, I didn't feel like there was much of a choice of when to take a mini-game. It was either right now, or if I was feeling adventurous, 1 more customer before I barely catch the end of the window to accept on level 20+ in progressive. This getting stacked 4 times means I don't get to space them out at all. Now that I'm using cheese greatest, there's a ton of leeway on when I take a mini-game and I can miss customers or mini-games with no real fear of losing. The perfect reload modification triggers after every few customers and makes up for any small slip ups and "More cheese please" feels like a debuff if I were to take it. That might be a bigger reason to tone down reload frequency than the mini-games occurring so often.
I also wonder how someone new to the game will understand what's going on with mini-games happening so early. I picture them dealing with the inscrutable Pokerface, not quite spotting the customer countdown in the HUD, trying to read the score for the customer before it fades away, and having to deal with the urgent events as early as round 1 (which I've only run into once). I don't think the game needs more complexity that early for possibly the same reasons that you introduce more novel customers in later rounds. Maybe urgent events start after round 10 or some set number of total customers after you unlock all the customers? I'm very much thinking of this like the old single screen arcade games where you can gauge your progress by how much of the game's enemies you've seen (e.g. which fruit did you see in Pac-Man, did you see the flies yet in Mario Bros). I'm imagining someone talking to another player about making burgers in this game and the other person thinking they're being put on until they get good enough to reach that part.
Also, I'd love to beta test if you ever get something like that going! It's always fun seeing what you're cooking up.