Re: How can I fix this sim count issue?
You can have more than 80 played sims in the My Households tab of Manage Households (MH). If you look in the bottom right corner of the MH screen there is a drop-down button where you can select the Maximum Sim Count. Choices are 80, 150, 200 Max Recommended and Unlimited. Right above that button is your actual Sim Count. So, rather than deleting sims, you can change the Maximum Sim Count to something higher to 80. The number of sims your game can handle is more or less dependent on the capabilities of your computer. If you have a low-end computer, then it's probably best to set your max sims to 80 but if you have a high-end computer, then you can run with Max Sims set at Unlimitied with no problem. Bottom line is that you need to experiment with the Max Sim Count setting to see what works best for you.
As you figured out, the Sim Count only includes sims kept in the My Households tab and doesn't include sims in the Other tab of MH. To move sims from the My Households tab to the Other tab in MH to make them unplayed and not count in the Sim Count, all you have to do is click on the little heart in the lower right corner of the household portrait in MH. The household will moved to Other automatically when you do that. If you want to move them back, all you have to do find their portrait in the Other tab and click the heart again. The max sim count number will change when you move sims between the two tabs.
Hope this helps.