Hi kobec,
There is no rigid “line” where something suddenly turns from “good” to “bad”. The guidelines are 3" or preferably less (2" for example would be better) but when there is only a small variance then your own best judgement vs the cost of making changes is the only way to decide.
If I were to say 3.25" is fine then the next question would be … “what about 3.5?” … quickly followed by “what about 4” etc and the guideline would serve no useful purpose.
It’s similar to any guideline such as the one for the minimum density of memory foam which is around 4 lbs. There are some mattresses which use memory foam that is in the upper range of 3 lbs and while the guideline won’t change … some people decide that memory foam in the upper 3 lb range is “close enough”.
So these kind of questions have no quantifiable answer and no consensus and the only meaningful answer would be “maybe yes maybe no” depending on many factors including weight, use of the mattress, the width of the slats, the specifics of the wood, and others including the degree of risk you are comfortable with which is getting down to microdetails that really can’t be quantified or predicted.
I would think that .625" gaps would certainly allow airflow.
The slats in the middle third under the heavier parts of the body would be more important.
You can see my thoughts about adding plywood in post #10 here.
Some of the suggestions in the post about wire grid frames may also be helpful if you decide that the current gap is too risky for you.
Phoenix