I kind of think 4-6pm is sometimes quite busy too depending on gate allocations as there are a few evening US departures, as well as the bulk of incoming pax from European/other long haul arrivals connecting onto regional flights. Have certainly seen Bridge (right hand side) to full capacity at that time. Pier F gets some of this madness too once in a while.

But generally speaking OP should be fine. If OP wants the spa appointment, I'd go to Pier and book ASAP (they now allow scheduling in advance within the day, as far as I'm concerned). Showers at both lounges should not require any waiting much, even when lounges are at full capacity. Dinner time at the Wing (before the evening 'rush') is almost always quiet.