you need to start at the beginning again, and check the battery completely, and get this "pickup and take to shop w/loaner" (not _rental_) in writing, with complete and clear understanding about who is paying the transportation and rental expense costs. To me, this seems like the standard answer when the inexperienced but available tech is sent to a job that is over his head/training level, get the truck to the shop where we can blame whatever we want, since no one is able to see what we are doing at the shop.
I might ask the 'Service Manager' just what it is that they think they can do at the shop that they can not do at your location, as far as an accurate diagnosis, (pull the battery out if this is your only forklift would be a good answer for that question).
What you are describing, contactor chatter and drop out when loaded, to me sounds a lot like the battery power is dropping out. can you get a good charge on the battery before the next person come to look at this machine?