I have no ideas about egg free, sorry, so some of these won't work, but may be worth investigating.
Have you a prescribed dairy free milk? (ie formula?) If not, you need a milk substitute. Personally, I'd avoid soya initially - you've already mentioned you hope soya isn't an issue, but unfortunately soya and dairy often (not not always) go hand in hand. We were also advised against soya for under a certain age - you may need to read up on that. We ended up on oatly (calcium enriched) milk. They also do a cream, iirc. Look with the UHT milks.
You also need a dairy free spread - pure or vitalite.
Do you make the cookies? my dark choc chips are only "may contain milk", so if you have an egg free recipie, you can substitute milk choc for dark, oatly for milk, pure for butter, and your there.
Rich tea biscuits and borbons are also worth a packet read - some brands are dairy free. No ideas on egg free.
meat, veg, potatoes
pasta and mince or tomato sauce
these look egg and dairy free fish fingers
You can buy free from cheese, so could make pizza. We never tried it.
Fish - tinned tuna for sarnies.
sardines or beans on toast
peanut butter (and other nut butters)
We got through quite a few avacadoes - good fats
Jelly for pudding
Will keep thinking - we did quite a few agg meals, but I'm sure there were lots that were either egg free, or easy to substitute.
Would skips or the dreaded MN pombears be an alternative to the watsits?
We were in a different place - dairy free from 2nds week of weaning, so just didn't introduce free from alternatives, except for oatly and pure. I didn't venture into the free from isle.
Good Luck.