Ian, I have some experience with old parlors in general but not specifically washburns so take that into account. That said, I don't recall ever seeing any parlor size guitars from this time that had more radius than can accounted for by tension on the bridge. Don't quote me but I don't think that (pre)arching a top was something that was being done then so that most guitars were pretty much flat on top to begin with.
Remember that all of that is based on my limited experience so it's completely possible that someone with more experience will come along to explain just how wrong I am.
My 1907 Washburn parlor's top is flat.
I think the arched back is a much a much earlier feature. I've seen designs/drawings of Baroque guitars with arched backs so I think that it's possible that a truly flat back is probably more rare than one with an arch.
Ian, here are some shots of a ca 1900 Washburn. The backs were radiused in both directions for structural and tonal reasons. The top, even though this one has a 'bubble', I would treat as flat, for your repair. Under tension it will form its own 'dome'. These guitars are built very lightly, and very well built, with top shelf materials. Tom
The example I pictured above measures: 6 3/16 x 15/16, 3/8 tall at the saddle, and the 'plateaus' measure 11/16 x 3/4 and rise 1/4 above the top, although these dimensions likely vary from guitar to guitar, but that's something to work with.
Tom is very close with his measurements, and I agree that the tops are pretty flat. The pictures are of 2 NOS Washburn bridges, one used bridge, and one on a guitar. The measurements are all very similar for all 4 bridges:
0.210 thick at truncated pyramid
0.300 thick at front edge of "plateau"
0.390 thick in front of saddle
0.225 at back edge of "plateau"
0.120 at thinnest between "plateau" and truncated pyramid
0.667 width of top of pyramid
0.825 length of top of pyramid
If the bridge pin holes are not evenly spaced, that is, they are spaced 3 and 3 with a wider section in the middle, then you may have had a "Durkee Patent" bridge. Let me know, and I will take a picture of that.
The last picture:
I bought that guitar in a pawn shop many years ago, and it had steel strings on it at the time. It seems to tolerate them, but I always use extra light strings. I suspect that like most guitars of that era it was meant to have gut strings.