It’s been a long while, but I think you can take a Malaysian taxi from Senai (definitely was possible *with a pre-booked taxi* from anywhere in JB to Queen St. before) to Singapore directly, not only to the Causeway to get a bus.

Not sure if it would require a Queen Street depot drop off + a Singapore taxi after, or if the Senai taxis will still take you directly to where you want to go.

Yes, crowds will likely not be an issue into Singapore. Currently, even the other way might still be fine at that time; in general, I don’t think traffic across the border has picked up to where it was before yet.