I was able to write my query against the VarChar(4000) data type. This worked.

Update [WBPROD].[dbo].[TASK_SCHEDULE]

Set TSKSCD_DESCRIPTION = Replace(TSKSCD_DESCRIPTION, '<timezoneId>0</timezoneId><timezone>America/New_York</timezone>', '<timezoneId>1</timezoneId><timezone>America/Chicago</timezone>')

Update [WBPROD].[dbo].[TASK_SCHEDULE]

Set TSKSCD_DESCRIPTION = Replace(TSKSCD_DESCRIPTION,

SubString([TSKSCD_SCHEDULE], CHARINDEX('<time>', [TSKSCD_SCHEDULE]) + 6, 8),

Cast(DateAdd(hour, -1, Cast(SubString([TSKSCD_SCHEDULE], CHARINDEX('<time>', [TSKSCD_SCHEDULE]) + 6, 8) As Time(0))) As Char(8)))

Where Cast(SubString([TSKSCD_SCHEDULE], CHARINDEX('<time>', [TSKSCD_SCHEDULE]) + 6, 8) As Time(0)) >= '01:00:00'