The only thing I would spray for this late would be croton (goatweed) and only if it hasn't already seeded out and the only reason I would spray it now is to prevent it's seed formation.
No set 'time' for spraying here in San Jacinto county. Spray according to the growth stage the weeds are in. I used to try to be thru spraying by late April-early May but some years, the goat weed hadn't yet gotten into the early growth stage and I'd end up spraying again if I had already sprayed for early stuff like tallow, seinna bean, dog fennel, and blackberry.
Now, I just wait till I see goatweed in 3 leaf stage and generally get everything with Remedy/2,4d mix. Risky tho, if we have a lot of rain and I can't get thru the lower end because of soft ground at the right time....
Too many factors to consider to put any set time on it. Depends when spring gets here, rainfall, how bad winter was (didn't have one this time around)
If your goatweed is mature and full of seeds, I sure wouldn't mow it, but that's just me.