I wouldn’t worry about 7-day-apart poops in a breastfed baby at all, especially when they’re not coming out hard and aren’t painful to move. But since you notice the increasing gas and discomfort, it’s worth investigating to see if you can’t help him to be a little more comfortable. I’m sure he’d appreciate it. The probiotic is a great move.
I think that in this case, mostly I’d try treating the symptom and see how things go. You know you don’t want to give anything to an exclusively breastfed baby that would contain any free iron, so this precludes prune juice, any herbs, etc. Giving anything with free iron is like starting solids; it’s the end of the virgin flora that is so protective for infants.
With that in mind, we are left with some non-digestible sugars that are sometimes used for constipation in infants. Lactulose would be the preferred choice. I’d mostly reserve this move for a true case of constipation but you might try the smallest of doses to see if it works out well. It could cause even more gas, or it might draw enough extra fluid into the intestines to move things through before gas can develop.
Exercise and abdominal massage are the most “non-invasive” options and probably what I’d try first in this case. You’d want to apply deep pressure as you move up his right abdomen, work more lightly across the top of the abdomen, and then apply deep pressure down his left side as if you were trying to scoot something deep out of there – because you are. Doing bicycle movements with his legs and pressing his knees to his chest can be helpful. Find ways to get him to exercise his legs himself too, whether he’ll do it laying on his back when given the right entertainment, scoot himself a bit when laid on his tummy, or dance a bit when you hold him up “standing.” Vibrating chairs are great for gas discomfort and sometimes also help the bowels move.
One more option is to insert a lubricated Q-tip or rectal thermometer just a tiny distance into his anus and wiggle it around a bit to see if it doesn’t start something. If this isn’t enough, you can use a nasal suction bulb to squirt a little bit of warm water up his rectum.
You are right that infrequent poops can occasionally be a sign of food allergy. If it were the case here, it’d be a very mild one. There don’t appear to be any other signs of allergy. The mildest allergies are the hardest to find. If you want to investigate, cow’s milk is the most common allergen for babies so I’d target it. You could do a short trial of 100% no milk ingredients in your diet for, say a week. Then a good way to really test is to have a much larger than usual dosage of dairy for a couple days after the elimination trial. See how all that goes. If nothing changes during either trial, I’d say there’s no food allergy here.