Wayne, if the breech blocks match the action, then it would have been a special order #4 since I seem to recall it has DST? Or since barrel and stocks were replaced it more likely was a #5 Pacific action, and got fitted with a new barrel and stocks. Once they're restored and reworked it's tough to say which model it once was. We can eliminate any of the pistol gripped models, or engraved models, or deluxe models. But #4, #4 1/4, or #5 Paicifc could all be candidates it was built from.
With the late action, and serial number it's very close to the end of production, and probably around 1889.

I've never seen or owned a Ballard with a serial number over high 36,000 range, and if I recall correctly John Dutcher also confirmed this to me when he was looking at a lot more Ballard rifles than I had. I surely haven't seen on in the 37,000 range.
Of course there are JM Marlin and Marlin Firearms Co. marked Ballard rifles that have the same serial numbers since John Marlin restarted numbers when he incorporated in 1881. I had a #6 Schuetzen JM marked, and a #2 Sporter MFC marked with the same number. Both were around the 3000 serial number range if I recall rightly?
I've seen some JM Marlin marked pretty high, but mostly they stopped around 9000 range. I have a weird #3 .22 Long that has all MFCo. features, but has a JM Marlin rollstamp, and is in the 36,000 range. It went to England and has Birmingham proof marks. Obviously a very late Ballard, and likely a receiver that got stamped early, and then lost or set aside until the end when they were cleaning up the last Ballards. It's also got a shotgun buttplate and stock instead of the standard crescent. It's the same buttplate as my #7 Long-Range, and weird on such a small #3, but serial numbers all match on stock and forearm to the gun. British hated crescent buttplates.