I've been testing out an old Iver Johnson 55A.  I like it, but it's been shooting very high, using .22LR high-velocity rounds.  If I switch to subsonics, shorts, etc., will it shoot closer to point of aim?  Is there anything else I can do?  It's a fixed-sight model, and I don't know if I can get a taller front sight for it.

How high at what range? Yes most of the older guns were designed around standard velocity ammo and that is what I would try first

I think I was around 10 yards.  I wasn't doing any serious match-grade work, just plinking and such (trying to see if I could take out small game with it).  It makes sense that the older guns were made for slower ammo (I think shorts and longs were more common than they are now).

Back in the day the cost of 22 ammo was cheapest to most expensive shorts longs long rifle standard velocity and finally high velocity long rifle which is the exact opposite of this day and age where ( current ammo shortage excepted) high vel is the easiest and cheapest to find

Try high speed ammo like a CCI Stinger. Usually a lightweight bullet moving faster will impact lower because the bullet leaves the barrel when it's lower in recoil. Look at the front sight for evidence of filing. Someone may have filed it down thinking that would lower the impact, which would have actually raised the point of impact.

What grain were the rounds?
Lighter bullets tend to group lower than heavier ones.

AT 10 yards, it won't matter what velocity.  You will need to raise up the front sight.

Any idea on how to raise the sight?

On a top break revolver there is not much you can do with the rear sight.  On a front sight to move the bullet  point of impact moves the front sight opposite of where the bullet strikes.  Needing a taller front sight can be achieved by milling off the fixed front sight and putting a grove in the top strap then pinning a new front sight in place.  If there is enough room you can mill off the front sight and cut a dovetail into the top strap and drift in a new sight.

If you know a very good welder he might be able to build up the original sight.  Go high then file down to zero the gun.  You'll then have to try an  re-finish the sight.  I don't think there is a lot of collector value on IJ top break but any change might affect the value, good or bad depending how well any change is executed.

This is actually a solid-frame (not a top-break) revolver.  After putting some thought into this, I think I'm gonna try building up the sight with some epoxy, then filing it into shape.  I can paint it flat black if it isn't dark enough.  Based upon the drawing that Numrich has, the factory front sight CAN be removed, so plan B is making a new sight from brass or aluminum, then painting it.

I got around to testing out the IJA revolver with some Aguila Colibris (primer only).  It actually shot low with those.  So, I think if I find the right ammo, it'll be gtg.