I can tell that you feel hesitant to use a crate, but the suggestion to get your puppy used to it during the day can really help. Something like treats, or raw bones, or a peanut butter filled kong with you sitting nearby with the crate door closed for something like 5 to 10 minutes will help. You would be nearby to ensure he doesn't hurt himself and to let him know that you are close. He really does sound lonely. We had Gilly in a second floor apartment that had no elevator, so until she was about 50 pounds, I carried her up and down the stairs for all but one or two of her potty breaks (the first week, this was every two to three hours, including at night, whether she was whining or not). I am glad I taught her to do the stairs because even when she was older she still barrelled down the stairs dangerously for the longest time, but it would have been worse if started later. But, if you have a "no dogs upstairs" rule, then maybe you don't want to start that anyways. If it's just concern about his joints, personally I'd just carry him up and down most of the time. She stayed in our room with us only until we were sure she would be safe in her crate (which we had partitioned for her safety and comfort to about a quarter of its original size) and until she was comfortable in her crate, then we moved her a little farther away and ultimately into a room farther away from us, where we wanted the crate to be. It took time and she exhibited many of the same signs as your pup. She was a few weeks older though. It took me several days (with me in the house or in the room, just sitting calmly reading not doing anything "fun"and her in the crate, closed door) before I knew she would settle and I could leave her. Now, if you're not comfortable with him in your room and you're not comfortable with him in his crate, but you don't want her to cry...you'll have to make some sacrifices at first, like sleeping in the kitchen. Either you or the pup is going to have to do something "uncomfortable" for the first little while until everyone trusts each other and feels safe. The first weeks can feel like forever, but in the scheme of things they're very short and his crying will stop relatively quickly. He's still just learning that you're his new family and whether or not he can trust you, and that he's lonely. Potty training might take longer though...
Also, ultimately Gilly didn't LOVE her crate, and after she was house trained and I knew I could trust her not to eat random things, she was left out of her crate at night and now she goes wherever she wants in the house. But, the crate or the kitchen will be the best place for your pup to house train...the smaller the area the better - maybe you an cordon off a smaller part of your kitchen, so the pup feels like it's his own room and will be more hesitant to pee or poop in his "crate".