do you really think it is a memory problem?
The error you quoted is pretty much unequivocal. Access thought it was out of memory. The only ways that can happen are that you are out of physical memory or you are out of virtual memory. The errors for "out of resources" is a different issue.
If this is a stand-alone DB OR you can MAKE it stand-alone for a while, you might try another approach.
Export the table to text using a comma-delimited format (or some other character that doesn't occur in your data, like | or ~ or ^). Export the table perhaps using a query that formats the output of your changing field to be consistent with the new format. ALSO export the table sorted according to the prime key of the table. (Don't trust this to luck; explicitly select a SORT order.)
Create a new table with the correct data type for each field (the type you wanted, not the type you had before.) This table will be empty. Define the prime key.
OK, now import the text file to your DB using the "import to existing table" option. This doesn't involve as many intermediate entities inside the DB, so it minimizes the growth of the DB.
If THIS fails, something else you said becomes significant. If you don't have the rights to do a DEFRAG on your assigned computer, the question arises as to what ELSE you are not allowed to do. It sounds as though your domain security folks have imposed a restricted environment on you.
If so, your next question is to the domain security guy to find out if they have forced a profile on you that limits virtual image size. This is entirely possible. If the answer is "yes" and the limit is something like 256 MB, there's your answer. It is not unusual for the data change you described to grow a DB by 100% ('cause from the sound of it, your big table is most if not ALL of your DB). And twice 142 is bigger than 256.
If THIS is your problem, you might need to export ALL tables from the DB, do the data changes in a NEW db, and re-import the tables. But before I would go that far, I'd talk to my domain security manager. And to my boss if the domain guy won't budge. 'cause you have a case where your security is now standing in the way of doing a legit and documentable job. (It's not like you were importing and embedding porn pix in your DB, after all...)