I had this same issue, as I had an old tamer and a new spot I could use for a new gargoyle character.
What I did have was a second account with a tamer. I sat the tamer on the second account at the animal tamer, logged on the first account, transferred the pet to the second account, soulstoned taming and lore, logged into the new gargoyle and picked up taming and lore and the pet.
Rinse and repeat as necessary.
It took a little while and I had to wait a week for the pets to bond again, but overall being able to fly next to them (especially a greater dragon) made it worth the time spent
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