Laminated card works well enough for one day and you can forget about having to gather them back.
If you do want something re-usable (which means getting it back after) look for a local printer that can do thin plastic.
alternatively do them all by hand, 200 won’t take a couple of you with permanent markers or spray paint and number templates that long…
Oh and make sure whatever you do you run off some blank spares and have a marker ready for a bodged board, there’s always one…
As for having the timing tags I’d say mounting them down in the BB area rather than up at bar level backed onto a number board would be best (IPICO are the ones that use proximity to an antena mat right?) mounting them too high is a recipe for timing malfunctions IME….