  Bright, high redshift ($z>6$) QSOs are powerful probes of the ionisation
state of the intervening intergalactic medium (IGM). The detection of
Ly$\alpha$ damping wing absorption imprinted in the spectrum of high-z QSOs can
provide strong constraints on the epoch of reionisation (EoR). In this work, we
perform an independent Ly$\alpha$ damping wing analysis of two known $z>7$
QSOs; DESJ0252-0503 at $z=7.00$ (Wang et al.) and J1007+2115 at $z=7.51$ (Yang
et al.). For this, we utilise our existing Bayesian framework which
simultaneously accounts for uncertainties in: (i) the intrinsic Ly$\alpha$
emission profile (reconstructed from a covariance matrix of measured emission
lines; extended in this work to include NV) and (ii) the distribution of
ionised (H\,{\scriptsize II}) regions within the IGM using a $1.6^3$ Gpc$^3$
reionisation simulation. This approach is complementary to that used in the
aforementioned works as it focuses solely redward of Ly$\alpha$ ($1218 <
\lambda < 1230$\AA) making it more robust to modelling uncertainties while also
using a different methodology for (i) and (ii). We find, for a fiducial EoR
morphology, $\bar{x}_{\rm HI} = 0.64\substack{+0.19 \\ -0.23}$ (68 per cent) at
$z=7$ and $\bar{x}_{\rm HI} = 0.27\substack{+0.21 \\ -0.17}$ at $z=7.51$
consistent within $1\sigma$ to the previous works above, though both are
slightly lower in amplitude. Following the inclusion of NV into our
reconstruction pipeline, we perform a reanalysis of ULASJ1120+0641 at $z=7.09$
(Mortlock et al.) and ULASJ1342+0928 at $z=7.54$ (Ba\~nados et al.) finding
$\bar{x}_{\rm HI} = 0.44\substack{+0.23 \\ -0.24}$ at $z=7.09$ and
$\bar{x}_{\rm HI} = 0.31\substack{+0.18 \\ -0.19}$ at $z=7.54$. Finally, we
combine the QSO damping wing constraints for all four $z\gtrsim7$ QSOs to
obtain a single, unified constraint of $\bar{x}_{\rm HI} = 0.49\substack{+0.11
\\ -0.11}$ at $z=7.29$.
