He has been bad with crying if I'm on the other side of a baby gate from day one. I've always been strong and ignored his cries but it still happens.
Unfortunately the risk of this very outcome is exactly why reputable trainers/behaviourists recommend against using the "cry it out" method. Whilst it works for some dogs, for many (particularly if they're sensitive, which whippets tend to be) it just very effectively teaches them to associate being alone with being in distress.
Are you able to go right back to basics with him and start only leaving him for what he can cope with (which may be as little as stepping across the threshold then immediately back into the room with him)? The difficulty with dealing with distress when they're alone is that whilst they are upset they're not in a fit state to learn anything so you really need to avoid putting them in that situation whilst you start from scratch and build their confidence up. This guide is specifically about crate training but it also covers teaching a pup to be left alone happily and you can use those methods however you choose to leave your pup. The aim needs to be never getting to the point where he's crying/barking/showing any signs of distress. This article on separation anxiety (as well as those linked to at the bottom) is also well worth a read and there's a section on the use of medication to help the issue.
I've been where you are now with DDog2. All the advice we were given back when she was a puppy (she's an old lady now) was to ignore her crying and, sure enough, we ended up with a puppy who was so distressed at being left alone she was busting out of crates and screaming herself hoarse. We had another dog at the time and she clearly took absolutely zero comfort in his presence, thankfully he didn't pick up anything from her but when the problem is being away from people another dog isn't necessarily going to be remotely helpful and it's very easy to end up with two dogs who cry when they're left. Another risk with using canine company as a crutch is that if it works you can be right back at square one if they ever need to be separated for things like vet trips, training classes, etc.
We did sort the problem out. I'm not going to lie, it took a while and was a lot of work but we got there and for many years she's been absolutely fine being left and is perfectly happy whether she's in the company of our other dogs or completely alone. We went right back to basics with her and left her as little as possible, building up very gradually from just a few seconds alone to longer and longer periods. Even with complicating factors (having left her mum/siblings too soon which predisposed her to attachment issues and being naturally very anxious/neurotic) she learned to be happy being left and if she can then pretty much any dog can!!