Answer: While there is perhaps divided opinion on this topic, in my experience English ivy does not harm healthy trees providing it is not overwhelming the canopy. For this reason I would probably suggest replanting with ivy and being careful not to allow it to climb the tree. Another possibility would be vinca minor (periwinkle) which is a non-climbing evergreen groundcover.
The plants you listed can be good groundcovers under some situations, but in this case I suspect the the tree will provide too much competition for water and nutrients -- both by virtue of the canopy and the roots. To make matters worse, the roots will grow to the surface in response to water and soil improvement, so your chosen plant needs to be a tough survivor so it can establish itself quickly.
Some of the stoloniferous hostas might be an exception and worth a small experiement to see, but in general hostas really do best with adequate water and nutrients at least until well established; Lily-of-the-Valley prefers a moist rich soil and will turn crinkly brown if it dries out or the summer is too hot; and caladium is a tropical bulb requiring lifting each fall and replanting late each spring after all danger of frost. It too prefers ample water to avoid going dormant in midsummer. Ferns are generally plants for humusy, woodsy soil and cool shady spots -- one exception to this might be the hay scented fern since it can be very aggressive in favorable spots and yet again, I fear it it will brown out in midsummer in such a dry spot.
Good luck with your project!
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