Okay I have 6+ E46, E39 & E53s, and have done a lot of work over the last 10 yrs.
Engines replacements, manual swaps, clutch jobs, rear ball joints (E53/E39)

Removing a stuck axle in an E53 from a rusty state is tougher than any other jobs I have encountered. You don't really know if you will ever get it out, and if you do, what collateral damage there might be.

I finally got mine out today (front driver's side) using a free hub puller from Advanced Auto - Only one they had fit - I torqued it up, then hit it with a 4 lb hammer. I worried I might break the tool. This was after 1 1/2 days of trying other methods and lubricating

I attempted to use Andrew's method of a 3/4 long bolt, an iron 1" pipe flange, but I need longer M14x 1.5 threaded bolts for the lug nut holes as my lug nuts weren't long enough..I couldn't get them quickly. This would definitely be a more powerful/durable set-up than the hub puller I used.

Here are my tips:
- wire brush and lubricate all exposed threads on ball joints and suspension bolts
- leave all ball joints intact and go after axle first
- Remove speed sensor and flood the insides with penetrating liquid.
- you may have let penetrating oil sit for a day or two
- loosen both strut nuts and remove the upper strut bolt and nut. Tilt knuckle forward
- Install Hub puller, torque it up with a breaker bar, and start swinging with a hammer.