Hi Leslam - thanks very much, I am not sure we can prove this 100% either way and I have set out my case on the Panorama thread so won't try to replicate here.
What you suggest is certainly possible. However, my opinion is that the spire in the engraving appears to me have a domed roof held up by pillars or spandrels. St Paul's is a beautiful building with a pointy spire. The approach to the church area in the engraving looks to my eyes to be slightly uphill across fields. I think St Pauls would be downhill from Ann St and would probably be fairly built upon by this date. The crane/winch and the conical-roofed building in the engraving are in the immediate foreground, and although I think the suggestion of an Amphitheatre in Livery St is a genius idea, both it and the Wharves must be 1/2mile or more away from Ann St.
For me, the winch indicates that the room is a upper garret type room, St Philips is the only domed church I can think of in the area held up by spandrels, it was flanked at this stage with houses on Temple Row West and there were open fields between them and Ann St in 1821 (see Lines Painting which also explains why due to lease restrictions). The Panorama at the top of New St would be just across the Rd from the position of the Manufactory, but as New St slopes down then you would only see the conical roof and a glimpse of the supporting rotunda from the top Room of a building on the ridge of Ann St. For these reasons (and more on the other thread) I think the inscription is wrong - perhaps that alternative view could be seen out of another unshown window?