Attn All that have posted advice,,and other colorful commentary...
I solicitied the assitance of another friend who has considerably more experience working on motorcycles than me, and he also has an impressive garage full of hundreds of tools as well.
He and I were finally able to align schedules and I took the bike over to his place last night.
Outcome: Apparently the rubber mallet that I was using was too soft. He used a more solid hammer and tapped the axle with what he described as his usual amount of force, and the axle came right out.
He was actually surprised that I had experienced any issues getting the axle out.
So - The bike now has a new tire, and is once again ready for the road.
Thanks to everyone who provided feedback and guidance -- much appreciated.
I was quite concerned, and was fearful of a bad and expensive outcome.
Luckily this time, the concern was unwarranted.