The Merge Geoprocessing tool will use the length of the first layer brought into the dialog. If every other parameter (besides field length) is the same, a simple (perhaps the simplest?) way that I have found to circumvent the errors that you've described, is to put the one with the longest field length in first. This is because it is using the first layer ...
In the catalog window you could do a right click on the layer you want to review and access the metadata, there is an geoprocessing history section with detail (date and time, tool used and parameters) you could export to XML or copy/paste.
More detail on that and on how to view tool execution history
Reading the answer you linked carefully you can see that you could copy the shapefile whose fields you are trying to change using the Feature Class to Feature Class tool.
This tool gives you a Field Map section with a list of all your original fields and the possibility to change the length property before actually copying the input sahpefile.
So basically, ...
I found a solution using a code to publish service from the Esri website. The code below uses python to delete a service by name.
The requests module works well with no errors while I faced problems when using httplib, urlopen, and urllib2 to send the request.
username = 'name'
password = 'pass'