Surely only Lake could be a request stop? Trains may need to pass one another at Sandown, and Ryde Esplanade and Ryde St Johns Road are the main stations for the town? Even if they weren't, you can't have a request stop at a station where you do crew changes.While it'd slow down the service for regulars, I think the best bet would be to do any work necessary to get the service up to a full 2tph up the pier, then to have the timetable offset 15 minutes from the ferries. It would probably reduce usage just for going down the pier (as it'd be quicker to walk), but most such passengers probably don't pay anyway, but would mean a better quality, less stressful connection for those using it to go further, especally with luggage.
Having now used it, there are definitely ways it could be sped up. Driver door operation would be one, as would modifying the doors to operate more quickly (I don't entirely understand why, but the conversion has resulted in them being slower than they were on the D78s as built). Making all stations except Brading and the termini request stops may also be useful, you could fit bus-style stop buttons on board. I doubt you'd need to eke much out to make half hourly feasible, which is what the idea was in the first place.
Alternatively just go back to the 20-40 operation, with the 20 gap timed to be either side of the main hourly ferry arrival (i.e. train arrives around xx50, ferry at xx00, train departs around xx10). This would mean a poor connection in the other half hour, but it's rarely actually half hourly these days.
So if it's literally just Lake why not simply remove the stops at Lake? It's not particularly busy or far from the other two...