I would expect the EV ZLX-12P to be able to cleanly play way louder than you can run them in a basement. You can only get so much volume in a small space. Above a certain SPL, you will get feedback. Feedback occurs because sound travels out of the speakers and is picked up by the microphone and amplified over and over again. The distance the sound travels from the speaker to the mic means some frequencies arrive out of phase and cancel, while other frequencies arrive in phase and add. My point here is the distance is an important factor in which frequencies are a problem and which are not. Some moving a mic or speaker can help.
The choice of mic and how the speakers are aimed can have an in impact on gain before feedback. The SM58 has a cardioid pattern, so the best rejection is directly behind the capsule. The problem in a small space is sound bounces of the floor, ceiling, and walls and travels back to the front of the mic, which is very sensitive. A mic with a tighter pickup pattern may help with gain before feedback, but they have two nulls of rather than one null at 180 degrees.
For example you could try a Beta 58 which is super cardioid. Super cardioid has a little tail at 180 degrees and the deepest nulls are at about 126 degrees.
This is the polar pattern from the Beta 58 Spec Sheet:
Try changing your setup and how the speakers and mics are aimed. Consider how you think the sound is bouncing around. In other words, try to figure out the path the sound is taking from the speaker to the mic. Also, if the speakers are used as foldback monitors, they should be placed in the null(s) of the mic.
Another thing you can try is using material to absorb some of the reflections. If the room does not have carpet try some area rugs. Other ideas including adding furniture with soft cushions or hang moving blankets.
I am not familiar with the mixer you are using. The last mixers I used were Yamaha LS-9 digital boards. The LS-9 was set up with 31-band EQs and also parametric EQ. Either can be used to ring the system and notch out frequencies that tend to feedback. Ringing a room works really well in larger spaces. It can help in small spaces, but not as much.
Basically to ring a room, you turn up the gain until the system is on the verge of feedback. Then you notch the frequency that is causing the problem. A notch is a narrow, deep cut.
In a small space the feedback comes on very quick and tends to be very powerful, which makes it more difficult to ring the system safely. If you allow the system to produce a super strong feedback spike, you may wind up blowing a tweeter. You should clear the room and use hearing protection any time you are ringing for feedback.
Proper gain staging and mic technique are some other important factors. If the gain is set too high the system will be more likely to feedback. Ideally the vocalist should sing very close to the mic with a strong voice. Then the gain can be turned down.
Singing close to the mic may make the voice sound too thick and bassy. This is normal and it is caused by something called proximity effect. The solution is to use EQ to correct the frequency response. Essentially you dip the lows using a pattern than is a mirror image of the proximity effect.
This shows the frequency response for the Beta 58, including the effects of proximity effect at different distances from the capsule.
The shape I use for the vocal EQ starts out like this and is tailored to the situation and the singer's voice.
Another gain related factor that increases feedback is clipping. In my experience, pushing part of the vocal signal path close to clipping tends to result in a lot more feedback.
So as you see there are a lot of things you can try. However, ultimately the best answer is probably for everyone to turn down to a level where the system can actually make the vocals clearly audible. IMHO, the only reason you typically need to play louder than this is because you simply enjoy playing loud. Playing loud does not serve any other purpose.
Keep in mind if you are playing too loud for the room and PA, it's not going to be very enjoyable for the vocalist. So in order for you to get what you want, you are essentially taking more than your fair share of available sound quality.