I would suggest not using the four inner screws of Connections. I understand that a lot of people use these (yep, after being cut to size ), but examining both a vintage screw and an inner connection screw will show you that the thread patterns are different. Using connection screws will eventually strip the plastic in your vintages, rendering all screws useless, which you will notice as time goes on.
I know the connection screw is suggested a lot, but a screw of another thread pattern will strip the plastic over time. I'm sorry but this is really the only advice I have - I do not know what make of screw can be used to replace vintage tamagotchi screws, and in addition, vintage screws are JIS though this may be irrelevant (I am not familiar with the range of philips screws that exist).
At the moment I am hunting for a bunch of cheap vintages to use solely for parts, as the four inner screws of vintages can also be cut to fit (and will be the correct thread pattern!). So far these are the only substitutes I can recommend. I'd go for P1s and P2s, as I've never had trouble with soft screws/broken heads with these, and are also the easiest to find