Hi MSTG007
We use Global Mapper software for this type of reprojection.
1. Import DEM (in native Lat Long)
2. Change Projection from Geographic or Mercator to UTM, change datum from Google Maps (sphere radius...) to NAD 83 (or NAD 84 CSRS in Canada), however always use NAD 83 to create Civil3D compatible DEM.
3. Export by window or polygon boundary, export to grid format (binary DEM) and select output grid x & y resolution (you have direct control over resolution, just may not make much sense to convert a ~10m dem to a 1m grid)
4. Done!
I'm from Canada, and the 1 arc-second SRTM DEM has only recently become available outside of the US. Where do you find 1/3 arc-second DEMs? (is this the same as USGS 3DEP?) I can't find it on the usual sources like USGS EarthExplorer.
Global Mapper can download from common online sources (or you can specify your own). I've downloaded 3DEP DEMs but these seem to have elevations truncated to the nearest foot, so not entirely useful for hydrology.