Solutions to the Red Supergiant Problem can be either observational or physical, and to date, both types have been proposed. Recent data and improved computer modeling have both helped make the later stages of red supergiant evolution clearer, leading to possible solutions to the problem.
Walmswell & Eldridge (2012) suggested an observational solution, namely, that circumstellar dust resulting from mass loss via the strong stellar winds of a red supergiant could lead to strong extinction in some cases, making it hard or impossible to detect the resulting supernovae. Based on data collected on 18 supernovae, they found an upper limit for the mass of a Type IIP supernova progenitor (at 90% confidence) to be around $27 M_{\odot}$, which would explain the dearth of detections of progenitors in the $16$-$30 M_{\odot}$ range.
The observational difficulties are moot if there is a physical reason behind the problem, i.e. if there is some mechanism preventing these red supergiants from undergoing Type IIP supernovae. Yoon & Cantiello (2010) suggested that red supergiant stellar winds could be increased to "superwinds" by envelope pulsations. This would lead to periods of larger mass loss rates than expected, followed by periods of smaller mass loss rates. This would correspond to oscillating around states of instability due to the pulsations, and would be prominent only in red supergiants of masses greater than or equal to about $19M_{\odot}$. The result could be drastic, with stars losing well over half their masses. The star could then evolve toward a Type Ib or Type IIb supernova.
Smartt et al. did consider the possibility of envelope loss in the paper you cited, but dismissed it as being unfeasible for a star in the mass range. However, it appears that they did not consider the superwinds induced by pulsations, making this solution feasible once more. It's also worth mentioning that the authors suggested direct collapse to black holes with at the most a very faint supernova; this idea had been explored in the past.