The minimum payout for Ethermine is 0.01, but you have to set your threshold in the settings… Go to ethermine and type in your address in the search bar, then go to settings, then click on “Gas Price Limit & Threshold” and set it to whatever you want. If you change pools before getting a payout you wont ever get a payout from the original pool if you didn’t reach your threshold. Switching the actual miner makes no difference, beside dev fee, and maybe give or take a few megahash. The higher your megahash, the more you mine, the faster you get paid.
Edit: I misunderstood your question. The payouts are handled by your mining pool. Most of the mining pools have a max payout and a min payout. I was talking about ethermine above, which I thought you were using. Just look up how to adjust the payout amount for whatever pool you are using. I’m sure you will be able to lower the threshold. Using different miners isn’t going to speed up your payouts unless for some reason your hashrate is way higher with another miner, which usually isn’t the case unless you have LHR cards.
As long as you use the same pool and address, you can switch to whatever miner you want.