Tiger you should look up the K66 as you would see a drain plug that is about 1-1/2" to 2" in diameter. Apparently you are just guessing at what needs to done and being too lazy to even look up the transaxle IPL on the Tuff Torq website.
Just can't change the filter without pulling the transaxle on early versions but later versions it is just a easily changed cartridge. With the number of hours if the drive belt and v-idlers haven't been changed recently it could just be a slipping drive belt.
Actually model and serial numbers are needed for proper IPL look up as to which filter would be used. Hopefully it is the cartridge type as in the left image.
View attachment 69382 or
View attachment 69383
It will require SAE 5w15 synthetic oil. And that plug should have a 3/8 square hole for a ratchet to fit. Careful remove that plug as that hole can be stripped out. Also all the dirt must be from the plug and surrounding area.
And if a shop not willing to do this oil change they are just plain damn lazy. It should be an hour labor plus the oil and filter if it is the cartridge type; longer if the other deep inside the transaxle type filter. But as said the filter don't have to change all the time just depends how bad the oil looks like. IF the shop are the least bit reasonable they will have a senior citizen discount like mine. I give the 65+ group a ten percent discount on repairs. Which here is basically more than just knocking off the sales tax.