However, for me I would need to see a clear connection between the specified geographic area and the church's arrival. If, for example, we have a reference to Philadelphia that predated the 1828 St Philips consecration this theory would be dead in the water. The absence of such a reference may simply be that we can't find one, not that one doesn't exist. Incidentally, how do you know that the church owned this land, certainly prior to it being entitled Philadelphia?
I could easily buy the delph bit as it seems almost impossible that early development in this area, be it industrial or residential or both, was not accompanied by some sort of digging or earthworks. It could be that such a dig connected to raw materials for local industry, such as iron-ore or coal. This said, I still find it too much of a leap to actually get to the name Philadelphia without the local name's 'inventor' being unaware of the Pennsylvanian place. This was clearly in existence by the mid-to-late 1700's. Not only that, but given Philly's role in the developing colony, I find it hard not to suspect that even in late-18th century England, including Sheffield, the colonial Philadelphia was quite well known here.
My hunch is still that there is a connection [if only by name] with Philadelphia, Pennsylvania. I agree with you that I doubt Sheffield's Philadelphia was so named because of some steel connection.
My suspicion is that our Philadelphia connects by religion. This might not be a formal link, for example between a specific Sheffield Quaker church and the developing trans-Atlantic Friends movement of the 17th & 18th centuries. However, it could be that local Quakers looked to important developments in Philadelphia Pennsylvania and took the name for their community.
For this, however, I need to establish that there is some Quaker connection with the land around Gilpin Street. This could be a place of worship or it could be a concentration of Quaker residents. In itself this wouldn't prove my theory, but it would be strong circumstantial evidence.
Another key might be if the Gilpin Street area was being developed at the same time as the big push in the US to have their Philadelphia as a key Quaker location. This period, from your helpful link, seems to be the late 17th century/early-to-mid 18th century. I would have thought that by the third quarter of the 18th century the still colonial Philadelphia would be fairly widely known in England, particularly amongst English Quakers. The Friends would probably have looked to it as a key spiritual reference point.
In my 1841 Whites Sheffield Directory it lists the following names which are initially listed under the road "Penistone Road" and then under a separate heading for "Philadelphia."
(Philadelphia)
Philadelphia Steel Works
Co.; J.J. Spurr, agnt
MOORWOOD J. tanner
ROBERTS A. beer house
LARNER H, beer house
RODGERS W, millwgt
OWEN R, cooper
LAROM Rev. C.
RAWSON Miss M.
SHAW Mrs. E.
IBBOTSON Mr. T.
DIXON J. vict
PEACE C. file mfr
FRETWELL Thomas
THOMPSON George
GREEN Misses, school
BATTIE A. bookpr
RILEY H, whsman
FLETCHER Rev. J., A.B.
LOMAS Mrs. S.
GWYTHER Rev, J., B.A.
FRITH Eliz. vict
All the names listed on Penistone Road before the Philadelphia Steel Works are listed with a house number but all the names after (as shown above) are not. I don't know if this meant that these people lived within the works grounds or that they lived on Penistone Road or the Philadelphia area, do any of the surnames look familiar?
I have just checked the directory section of the book and as an example it lists the following names from the list above,
PEACE, Charles, file manufacturer; house, Long Row, Philadelphia
LAROM, Rev. Charles, Baptist Minister, Philadelphia
RODGERS, William, millwright and engineer, Philadelphia
Did you know that
1) the name Philadelphia is derived from the ancient Greek term for 'brotherly love.'
2) the walls of the city of Philadelphia in Turkey are rumoured to be built from the bones of the christians that perished in the holy wars (actually a very porous rock)
3) Philadelphia was also an ancient city of Asia Minor northeast of the Dead Sea in modern-day Jordan. The chief city of the Ammonites, it was enlarged and embellished by Ptolemy II Philadelphus (285-246 B.C.) and named in honor of him.
4) In addition to the well known city in Pennsylvania, there are other US name-sakes in Mississippi, New York and Tennessee
5) Philadelphia, Pennsylvania the "City of Brotherly Love," was founded in the late seventeenth century as a Quaker colony by William Penn
6) In the UK, Philadelphia is a village in Wiltshire just outside Bath, a district in Newcastle and of course a certain well know location in Sheffield