I can see what you're getting at, so here is the breakdown I am thinking for gameplay.
In a arsenal package of rounds, nine rounds are normal, the tenth is a cleaner (historically with a reduced charge to scrape and leave less residue).
Let's say the average soldier can fire three rounds in a minute, which equals 20 seconds per round. After the nine rounds let's add three seconds progressively per round which equals roughly a third of a second times nine. The cleaner round cuts that over half to one seconds extra overall which starts another 10 round cycle. After 30 rounds, you take a singular "loading phase" to pull a greased patch, thread it through the ramrod and clear the bore and start your next 30 rounds OR attach a cleaning brush.
These times are examples for full length muskets.
.58 Caliber Base Reload - 20 seconds
First Cycle / 2nd Round - 20 1/3 seconds
First Cycle / 9th Round - 23 seconds
First Cleaner Round - Resets to 21
Second Cycle / 2nd Round - 21 1/3 seconds
Second Cycle / 9th Round - 24 seconds
Second Cleaner - Resets to 22 seconds
Third Cycle / 2nd Round - 22 1/3 seconds
Third Cycle / 9th Round - 25 seconds
Third Cleaner - 23 seconds
Greased Patch OR Brush Resets to 20 seconds.
.69 Caliber Base Reload - 20 seconds
Same premise, but instead of 1/3rd, make it 1/8th with no cleaners and a full reset on the 30th round.
If you're worried about the tactics, fire the rear rank, wait for half way in the reload, have the front rank fire or vice versa or fire by platoons. Automatic 10-13 second reloads for half your commands. The manuals of the period and previous spell this out very clearly even for the greenest Lieutenants.