The 9's and 10's should work together if you use the correct spacers between them. I've customized a 9-speed cassettes with one 8-speed cog but used the 9-speed spacer and it works fine.
As an expedient, you could remove one of the loose cogs from your current cassette and add an appropiate spacer and a 30T cog behind the 23T. This would give a big jump from 23 to 30 but would give a bail-out gear for the times you need it.