Fall is the best time to kill grasses. Summer broadleaf weeds can be a great addition to clover. Many are great deer food plus they help shade and protect clover in the summer. Here is my formula for establishing a perennial clover plot:
First, I want to start with a clean field. I'll broadcast Durana and Winter Rye seed without tillage, then cultipack and spray with 2 qt/ac glyphosate. This will kill burn down the field. I like Durana because of it's persistence and drought tolerance. I like 10 lbs/ac of Durana with 100 lbs/ac of WR. The Winter Rye acts as a nurse crop keeping weeds at bay while the clover is establishing. Durana is slow to establish, so one key is timely spring mowing. Each time the WR hits about 18", I mow it back to 6" to keep it from shading out the clover. After that first spring, I only mow clover once a year right before hunting season when summer weeds are about done and cool nights and fall rains favor clover. It bounces back and takes over the field again.
I am very weed tolerant, especially of warm season broadleaf weeds in general.
In your case, my advice would be to wait until fall. Spray with 1 qt/ac gly. This will kill grasses and top kill established clover. Wait until the clover has rain and is in good shape before doing this and when you have rain in the forecast. I would then surface broadcast WR and clover and cultipack.
This will take advantage of any of the clover that is well established as it will bounce back from the root system. It will give you an attractive field this year with the WR, and it will add new clover to the field. Use the same mowing I described next spring and then just let the field go mowing once before the season.
Remember, deer don't care about magazine cover plots. Many broadleaf weeds are both nutritional for deer and add structure to the field protecting clover from summer heat. Over time, clover fixes N into the soil attracting N-seeking plants like grasses. Any clover field will get more and more grass over time. There is no need to spray it in general. You fight a loosing battle and just play for grass selective herbicides. I get about 10 years out of Durana before the grasses dominate the field. At that point it is time to rotate the field into an N-seeking crop to use up that N. Buckwheat, Corn, Sorghum and Sunflowers are all crops that will benefit from that N. After a year or so of that, you can rotate back to a perennial clover plot.
Best of luck!