It is a long shot I'm afraid.
Tried Emkay, for example?
Or possibly, ModelFixings (though that company sells mainly metric sizes)?
If you end up having to convert the design to metric, you'd be looking at M3, 3.5 or 4, whichever would be the more appropriate, but for which cap-screws are readily available… e.g. from above?
Alternatively, try UNF cap-screws. These are still fairly easily obtainable (e.g. Westfield Fasteners, possibly those above), and if the engine is in Imperial sizes, at least the UN series is as well.
'
If you have already drilled and tapped the holes you would have to assess whether the replacement is close enough for re-tapping as-is to trim the thread, though that's a horrible practice leading to loose threads; or would need re-drilling and tapping for the nearest size M or UNF above. You might need re-cut the counter-bores as well.
One immediate barrier to the horrible practice is that although actually metric the BA diameters are integer mm in only some sizes, and the thread angle is about 47º whereas M- and UN are of 60º. It might just work for 5BA as that is very close to 3mm dia, (like 0BA / M6, allegedly) but I have not tried it, and would not recommend it for anything critical.
I think you are going to have to consult detailed thread-tables carefully to find a replacement, but the risk is ending up (as I have), with an inelegant mix of thread standards in one machine.