Seized front axles are somewhat common, on many machines.
Patience is your best tool. Try something, take a break, maybe leave it be for a week while thinking about it.
Sometimes, it comes down to what parts are sacrificial, despite your best efforts.
I think what gets many, if not most of them hung up is the bearing spacer. That's not a big deal if they're already out of the forks, as in depending on how the the axle is attached and if the forks can be disassembled to get the wheel off. That just leaves knocking the whole axle, bearing and all out the side of the hub it can come out of. Not the side that has a nut or axle head left on it, that hub bearing lip won't allow it to go through the hub.
If it's actually seized in the fork legs, that's more difficult. It may help to remove the fork so you can lay the whole assembly on it's side, so penetrant can pool and soak in instead of running off. Pop the outer bearing seals loose if possible and do the same with some penetrant.
You're correct, that's an awkward thing to set up in a press. Really need two people to do it unless building some sort of jig to hold it all true.
It's a good idea to look for replacement parts and their cost if it gets to the point you're fairly certain something will break and you have any control over what part that may be. It's not just that rust and corrosion has it seized, it's that it's mechanical when bad enough, the two pieces are just about one. I've got a couple parts I've taken a stab at for years, trying to save everything. I'll forget about them, then rediscover, and spend a little bit of time working. At some point I'll just start hacking away at the least expensive pieces to save what I can instead of ruining all of it.
I'm talking using air s, presses, the whole lot and nothing has budged. In the end, way more time spent than any of it's worth. It's just a matter of accomplishment now.
Good luck. I hope most of what I said is wasted and you get it apart and still usable. It's certainly frustrating when there's more involved and technical things to repair.
The story of three wheels and a man...