This boils down to a conflict of preference
Normally, I feel like "conflict of preference" sounds to contentious and presumptuous, but from what you're describing... I think it's the best way to describe it. You find preference in playing no matter what the circumstances. Your friend has clearly tried both ways and has burned himself out in doing so and overextending. It is the combination of factors that sounds like it is influencing his decision the most. As a result, there's a bad taste in his mouth from playing online due to the fact it inherently feels different than playing in person. I know this all sounds obvious, so let me skip ahead a little.
Your friend played both ways and burned himself out. Because he was overextending himself, his mind likely associated the method that felt different to him as being "bad different". As a result, he will be averse to the idea no matter what you say or do. He has a set paradigm that won't change until he chooses to make the attempt again on his own. Maybe you can convince him to play online with you guys, but if you do and it's not from his own eagerness, you can expect his experience with the game to be a bad one no matter how good you may think it is going. Each bad roll will compound and feel worse online than at a table because he already dislikes the idea of playing that way. If his character dies, you can expect exasperation and/or embitterment.
Essentially, the question you should be asking is this:
How do I find a middle ground?
To be honest, I don't know what to say to answer this new question. It's something you'll have to work out with him, ultimately. But I can offer some ideas.
- He says Voice isn't the same in person, so what about you suggest
doing it as a video call instead of a voice call? Sure, it's still
different, but it's more of a step between what you are doing and what
- He doesn't like the feel of playing online, so what about (if you do #1)
letting players choose to use their dice (on camera) or
the in-game dice roller? Sure, you can still weigh your dice, but
just keep an eye out in case anyone is getting suspicious rolls when rolling
Make an agreement to do monthly one-shots by alternating between online games and in-person games. You don't have to have people drive out every time and have a game at a physical table, but you can probably convince your friend to be involved in infrequent online games especially if you also do physical games as well. To reduce the drive time, you can find a location that lies halfway between you and your friends. Good places to look into are game shops (especially ones that host TCG/CCG tournaments), comic shops, public/national parks, or public rest stops (depending on the laws in your area).
(See here for a list of rules regarding parking time for rest stops organized by US state. Use this list as a general guide, but be sure to double check the information with your state before making plans.)
Even if you only manage to do an in-person game once every couple months, with an online game in the between-months, by choosing a location where everyone, yourself included, has to drive out to for the game, it shows you're just as willing to put in work for it as you expect them to be. Sure, you and your friends will still have to drive around 4 hours in this case, but those who participate should see it as a give-and-take and it can work as a good show of investment. If people can't make it to the games, it's nothing personal; not everyone can do 2 one-way 4 hour drives, even if it is only once every two months. But who knows, it may show to have other benefits for you and your friendships.
Anyhow, like most interpersonal issues, the solution boils down to 3 steps:
- Sit Down.
You won't be able to make everyone happy, and if he doesn't want to play online no matter what concessions you're willing to make... that's fine. Respect his choice, because ultimately these are games and should be fun for everyone. If he cannot find amusement in playing online, you're only going to be torturing him by trying to make him join the sessions without trying to resolve his issues to some small degree first. Obviously, you can't fix every problem. Sometimes, you have to cut players loose no matter how much you may want to keep them around. No matter what, though, if you really want him involved in your games, you should first try to make the format more appealing so that he isn't immediately turned off to the idea.
Put simply, if you were in his shoes, what would you want your DM and friend to do?