What could be causing my washer to make thumping sounds after the spin cycle?
Your washer is configured differently than the Whirlpool mentioned, but all washers are susceptible to drive and suspension issues. One of your suspension springs may be broken, or there could be a problem in the belt drive system.

The front panel should come off fairly easily, though it may be difficult to fully inspect everything without removing the other sides. The machine is still operational without the sides, you should be able to locate the problem by running it through the end of a spin cycle. Just be sure to stay well clear of moving parts.

If you can manage getting the panels off (locating all the screws can be tricky), and identify the problem, you probably can manage replacing the broken part. It is certainly cheaper than hiring someone, and it certainly does not warrant a replacement machine. (Unless you just want an excuse for a new machine)