Something that would help is if you could unlock more slots to select minions. Or select a minion as your favorite so you get it more often in the shop.
Like if you could spend cash to upgrade your shop and with it get access to better minions more often. Or to get two rows of minions, so you buy the upgrade and see 8 guys instead of 4.
If I want to do a themed build, I have to restart around the stage where you have treasure chests start to spawn because going further and saving my cash just means I'll get obliterated and lose.
The ideal strategy is when your favored minion both shows up, and you have enough cash to buy them.
The fact that the price increases by 1 to reroll, and it never goes down again means you should reroll a few times and then never again, as it's always worth it to simply buy another minion over trying to get a specific one. If you've survived long enough to have enough cash to keep rerolling, you might as well keep doing what you're doing.
Perhaps you could provide some sort of passive reward based on the amount of cash you've spent rerolling? Maybe a gacha system? A certain number of rerolls buys you a ticket to spend on rolling and earning a random minion. Or some other reward, such as the amount of cash you spent on rerolls X2.
These tickets could be another item that appears in the overworld on missions. Perhaps when you complete levels, too? The prospect of guaranteed minions and cash means people will have fewer burdens on their cash flow.
Have you considered adding resistances? Possibly certain minions could be resistant or immune to different kinds of attacks which will have a major effect on your strategy. So the bone minions could shrug off damage from archers while being weak against knights and neutral to wizards.
A similar deal for the mushrooms, being resistant to physical damage from swords but neutral to arrows and weak to wizard magic.
Another idea I had was “equips” where you have items that remain with you and can be given to a minion. Like a flag that makes the person holding it run faster and is dropped when they go down. So people pick up the flag and get their speed boost.
In reference to the other person's comment about upgrading minions or them providing bonuses for you having a lot of them. You could have a camp of some sort for each minion type that provides this bonus.
So a kennel or encampment for the dog types, and some sort of pit that the demons live in. A crypt for the undead.
These could be upgraded to provide progressively better bonuses and enhancements to units of their types as you invest more into them. You could also create a unity camp, where it provides a series of bonuses for a multitude of types. Rewarding you for having a varied crew.
Synergies, I mean. Like if you have mushrooms on your team, your undead will grow mushrooms on their bodies and become resistant to blunt attacks, removing their weakness.
Thanks for making this game. I enjoy it. I saw it on a youtube video that you posted in the comments of.