"...Would necessitate greater modification to the carriage aircraft," - Avro WRD report.
The W.110 dates from mid 1957, and appears in report WRB.4 in August 1957, which would post-date the P.176 as it was canned in April 1957. Gyron Junior was pretty much all that was available in the class. Info on the P.176 is in "A View from Ansty" by David Williams, RRHT No.25. Only a couple of pages but better than nowt.
Carriage problems had cropped up on the earlier W.107, which was even larger. The W.110 "length at centreline" was actually 42ft and so one suggestion was to reverse the retraction of the nose undercarriage to have it retracting forwards, or having it retract straight up, freeing up around 10ft of ventral real estate. The W.110 was installed nose-down as shown in the drawing from the RAF Museum.
One way to address all this was the Z.43, a W.110 scaled to 35ft. Neither the W.110 nor Z.43 could be realistically carried by Victor, which also needed the nose undercarriage moved and nose-down installation, which led ultimately to the W.110's demise.
Chris