Getting the correct altitude values
"Software for estimating the total ascent of a walk gives values that are too high if you use the track recorded on most GPS models.
The GPS system was optimised for best horizontal accuracy but still gives useful results for the altitude. However, the scatter on a horizontal track can usually be ignored since an energetic day in the Peak District will perhaps cover 20,000m horizontally. The equivalent vertical journey will be more like 500m so the scatter is getting serious and the vertical scatter is worse than the horizontal scatter! (This is why Garmin sells GPS models which track atmospheric pressure for the altitude values)"
Happily there is a very easy answer. You may have already visited the GPSvisualizer page. Near the top of the page there is a link called "Look up elevations". It takes you to the altitude-correction page where you will see a place where you can load your GPX file and then click on "Convert & add elevation". Try it! You will find you get the corrected file delivered back quickly with the old altitude values now overwritten. The new (replaced) altitude values seem to be accurate and reliable.
Here is an example of such a correction....
If you now want to sum the ascents and descents on the corrected file, then open the file in RouteConverter.