Effect of tailplanes. The report also concludes that horizontal tailplanes are largely
ineffective in improving the long term response of pitch dynamic stability (phugoid
mode). This is the result of studies primarily on narrow tandem cockpit enclosures.
A CAA Flight Test Specialist qualitative evaluation of the effects of a horizontal
tailplane on a single side-by-side configuration gyroplane type indicated a degree
of improvement in the phugoid characteristics at higher speed. It is appreciated
that in paragraph 8.3.1 (page 152) of the report it is stated that other factors can
affect the phugoid mode.
Phugoid is not, so far as I know the major issue with gyroplane LoC / in flight failure - that tends to be SPO related, sometimes with linkages to vertical motion of the pitch inceptor. IIRC, the Glasgow research papers (not the CAA interpretation) looked mainly at SPO and LSS, not the LPO, and were very much about modelling of gyroplane stability, not airworthiness recommendations, which were CAA conclusions (with the exception of the 2" rule of thumb, which IIRC did originate in Glasgow).
A tailplane is fairly self evidently going to damp the SPO, and thus will have a beneficial effect on the risk of LoC. Because the phugoid is nominally constant AoA, you'd not expect it to have all that much effect, unless it incorporated an elevator.
G