You are not using the table in Word for the intended purpose. What you are describing seems to be an Excel layout, and not Word. While Word will do some simple math functions, that is not the purpose of Word. You really should be using Excel to do the kind of math functions you are proposing.

In Excel, you can set up something that looks very much like a Table, but has greater math capabilities, and will update automatically. Word does not do that automatically. The formulas you have used can be used in Excel in the same way, and the Total will update the instant you make any changes.

I would also not try to create your document in one system and then try to convert it to another. It is much simpler, and less troublesome, to create your table in Excel right from the start, and it will work very well that way. You can then forward that to anyone else in Excel format, or create a PDF of your table and send that document. There are often some details that get lost in the translation from one OS to another, and it's best to avoid that, if at all possible.

While Excel may not be in your comfort zone, once you look at it, you will see that it is very similar to what you are using now, and is actually very easy to use, especially for the kind of work you are doing. It excels at that kind of work! (sorry for that pun)