Okay, cutting speed for 17-4 stainless is roughly 175-300 sfm, so you need to speed up the lathe. RPM = Cutting speed in SFM X 3.82 / D, where D = diameter of the work piece. So, say your work piece is 1.5" OD. The calculated speed would be somewhere near 764 rpm; this would be a good starting point for external turning. The problem is that we are not external turning; we're boring. Your boring bar is not seeing that 1.5" OD; it is seeing the size of the bore. So, say you started with that 0.385" hole. This would give us 300 X 3.82 / 0.385" = 2976 rpm. Note that as the bore size increases, rpm drops (EDIT: rpm is supposed to drop) until you reach your 1.24" ID, where lathe speed would be somewhere near 1000 rpm. Not only that but your feed is supposed to change with rpm as well. It gets complicated, and this is the stuff I left out of the boring article because it confuses folks.
So, how do you bore a stupid hole? The way I do it is to start with the starting ID and calculate rpm; in this case our starting rpm would be near 3000. Since my lathe cannot go that fast, I would start at the max speed my lathe can run, which is 2400 rpm. I would manually feed the bar because the hole is shallow, blind and because I can feed at whatever feed rate I need to keep up with the speed to produce coiled chips. As the hole gets larger, I cut my speed down IF I have trouble producing the chips I want. Sometimes in harder materials it can be difficult to keep up with the speed and this will cause poor finishes and inaccuracies in the bore. If this is the case, slow the lathe down a gearing step or two and that will allow you to keep up with your feed.
As I keep saying, the lathe teaches us to respond to the cut and this is one example of that. If you cannot feed fast enough to produce the chips you need, slow down the speed until you can.
One thing you must do when boring to precise depths is to use a carriage stop. Do not rely on a DRO; it is not precise enough. Use a stop. If you do not have a stop, buy or make one but get one and use it. I'm not trying to seem draconic here; not only will a stop improve the accuracy and appearance of your bore; it will prevent you from damaging your bar.
Not sure how the gun guys do this. Maybe post this in that subforum?