Please, go see a lactation consultant.
First, because these questions around pumping are best answered by a person with specialized training and information in the field. Their whole job is to help parents provide breastmilk for their children!
Second, since being on the breast -- even part time -- can increase supply, it's a good idea to give it another try. But as new moms (I only have one child), we don't know *why* a baby may not be latching.
Mine didn't latch because his tongue was so strong, he'd push the nipple out rather than drawing in. That's why it took four days to 'train' him to breast, and it involved using finger training and then nipple shields, and hten it was 5 weeks of nipple shields before he was fully on the breast! But I wouldn't have known this if I hadn't seen a lactation consultant. She identified the problem and gave us a workable plan of action in under 20 minutes!
And from her, I also learned to pump. I continued to pump even though we had him at breast because I wanted a milk bank, and good thing too, because my friend had extremely low supply, and so we were able to provide 1/3 of the food her baby got! She provided 1/3, and 1/3 was formula! When she went back to work, she stopped pumping, so then her daughter's diet was 2/3 formula and 1/3 what I pumped. I consulted my LC to learn how to balance pumping and nursing so that we could get everyone good nutrition.
So, a good lactation consultant is worth her weight in colostrum! <--- breast-milker's joke, there!
I would suggest, too, that having the baby on the breast will make things easier on momma. I know it made a massive difference for me, and my friend who went back to work when her son was 3 mo felt the same. She would pump during the day (for the next day's bottles), and then nurse her son at home. She would nurse overnight which kept supply up, and also made it easier the next day (it was less work to breastfeed at night than wake for a bottle). So, your wife might find it the same.
And please note that I"m not advocating for "ideal" situations. I'm simply asserting that the idea that "babies must eat at 6 months" is simply not the case scientifically.
If you want to feed your daughter, then certainly do so. And, you can go through any number of food introducing processes -- we did baby-led weaning. Another friend of ours is WAPF, so she did that process. I think you're sort-of doing (or your quesitons look like) allergen avoidance ones. All good.
I would recommend focusing on the breast milk/formula at this point, though, personally, because I have a prefernece for the ease and awesomeness that is baby-led weaning.