>> but I would really like to find another LA 608, if possible.
Hi Cindy, that new detail ("LA608" vs the originally typed "A608") actually changes things quite a bit.
The Maytag washers of this series were produced for about a decade, with the A608 model appearing in the last few years of that. The "L" prefix, however, indicates that your machine is the Light Almond color, which came quite late in the run as well, also only the last few years.
Almond machines in this series don't show up for sale very often. Combine the rarity of the color, with a specific model (A608) that was only produced for a few years, and your odds of finding one used like it, 40 years later, in good working condition, are a needle in a haystack. You might find one, but it might take years of searching to do so. And you might only find one in worse shape than yours.
So with that in mind, I would say your best bet is to either find a local repair shop to work on your machine, or dive into it yourself if you are mechanically inclined. Finding someone to work on it may be difficult - grab the phonebook and call every standalone Mom & Pop type place you can find, until you find someone willing to look at it.
The GOOD news is that the most valuable part of your machine is the cabinet and control panel, both of which could be swapped over to the mechanical guts of any machine from a 20+ year span as a last resort. So even if your machine is given a terminal diagnosis, you are still far from being out of luck. Of course doing this would still require a local service person willing to work on the machine...
Good luck!