Reionization-era galaxies tend to exhibit weak Ly$alpha$ emission, likely reflecting attenuation from an increasingly neutral IGM. Recent observations have begun to reveal exceptions to this picture, with strong Ly$alpha$ emission now known in four of the most massive z=7$-$9 galaxies in the CANDELS fields, all of which also exhibit intense [OIII]$+$H$beta$ emission (EW$>$800 $mathrm{mathring{A}}$). To better understand why Ly$alpha$ is anonymously strong in a subset of massive z$simeq$7$-$9 galaxies, we have initiated an MMT/Binospec survey targeting a larger sample (N=22) of similarly luminous ($simeq$1$-$6 L$^{ast}_{mathrm{UV}}$) z$simeq$7 galaxies selected over very wide-area fields ($sim$3 deg$^2$). We confidently ($>$7$sigma$) detect Ly$alpha$ in 78% (7/9) of galaxies with strong [OIII]$+$H$beta$ emission (EW$>$800 $mathrm{mathring{A}}$) as opposed to only 8% (1/12) of galaxies with more moderate (EW=200$-$800 $mathrm{mathring{A}}$) [OIII]$+$H$beta$. We argue that the higher Ly$alpha$ EWs of the strong [OIII]$+$H$beta$ population likely reflect enhanced ionizing photon production efficiency owing to their large sSFRs ($gtrsim$30 Gyr$^{-1}$). We also find evidence that Ly$alpha$ transmission from massive galaxies declines less rapidly over $6<z<7$ than in low-mass lensed systems. In particular, our data suggest no strong evolution in Ly$alpha$ transmission, consistent with a picture wherein massive z$simeq$7 galaxies often reside in large ionized regions. We detect three closely-separated ($R$ = 1.7 physical Mpc) z$simeq$7 Ly$alpha$ emitters in our sample, conceivably tracing a large ionized structure that is consistent with this picture. We detect tentative evidence for an overdensity in this region, implying a large ionizing photon budget in the surrounding volume.
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