I'd imagine Masquerain's best bet at using Sticky Web in the meta is attempting both QuiverPass alongside it. Yes, I myself said that it is too hard / near impossible for it to do, but that didn't stop Toxic Spikes + Sticky Web Ariados did it? The point is that it prevents Masquerain from being easily hard countered, as it can fulfill one of its two niches should the opponent have a hard stop to one of its moves.
QuiverPass + Sticky Web
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name: QuiverPass + Sticky Web
move 1: Quiver Dance
move 2: Baton Pass
move 3: Bug Buzz
move 4: Sticky Web
ability: Intimidate
item: Focus Sash / Leftovers
evs: 248 HP / 8 Def / 252 Spe
nature: Timid
The set may be tweaked (most notably EVs), but either a QuiverPass Masqy that threatens Web would make the best use of Masqy's qualities. Sure it has anti-lead moves such as Scald and Energy Ball but Leavanny does a far better job at that. It can either safely throw out Web turn 1, or if something like a Xatu, Cryogonal, or Mantine rears their ugly head, then Masquerain can instead resort to QuiverPass to remain useful, which is more than what can be said for other Webbers.