Not without doing a comprehensive search.   My BA collection might have a few, but they’re mixed in a box, and unlikely to be 90°.  Nor do I know of a supplier.

Could you substitute metric or US?  Problem is BA is obsolescent, mostly sold to support older equipment, and rarely used by industry in anything new.   It’s slowly fading away.

Back in the day, virtually every head-type was available off-the-shelf for BA, now only a limited subset of the common types.   Though there’s New-Old-Stock about or they could be made to order (£££), finding BA can only get worse as the years roll by.  On a new build, I’d think twice before adopting BA.   Nothing wrong with the thread, the issue is availability.

Dave

The only help I can offer is to try talking to Alan at EKP supplies, they are manufacturers and if the number needed was viable they might be able to do a run. Good Luck. Noel.

For that quantity, could machining a 10BA steel cheese head screw be an option? Rear tool to form the countersink; front tool to form the raised head. Convert the cross slide to lever-operated and use two stops. Lever operated collet chuck. Loading and unloading would take longer than the machining (stick with magnet each end and keep the spindle running).

Is the 100deg. csk. item that you have identified that critical? On such a small head, ~0.120″ dia., the under-head gap will be tiny and the more obtuse angle will ensure that the outer rim is bedded down.

An earlier thread on this forum was enquiring about the origin of M1.7 threads.
One of the comments, by David Jupp, was that early Olympus cameras specified metric, but in reality the threads were BA

Not sure if that’s any help, but Luton Cameras specialised in older Olympus, so they may have a supplier.

Bill