Don't know where your info is coming from, but JD parts are pretty easy to get.. next day delivery if paying shipping. Free shipping if on the dealers order every 2-3 days. Sometimes sooner if moved from a dealers other shop when available. No experience with the others you mention, but have heard the opposite for both of them.
What model Deere have you been having trouble with and what parts are not available?
Service will depend on the dealer I believe, and will depend on their workload from other customers. A customer like myself who purchased my JD 4300 22 years ago and has been a great tractor with essentially no problems, I'd expect isn't on the top of the list to get service compared to the local farmer who owns several JD tractors and other expensive machines and depends on those machines to operate non-stop day in and day out. At least I would expect that would be the case for all dealers.