Too many Big items - must get rid of one

[ComBAT]

Good morning,

I was struggling to find old forum topics on Big item discarding scenarios because the search is limited to one word of 4 or more characters, so my apologies for starting a new thread.

I have 2 big items in play for whatever reason I am legally allowed to have more than 1 for. A card is played on me that makes this arrangement illegal... let's say I am cursed to lose my Dwarf race...

I am not the lowest level and more than one player is tied for the lowest level.

I know that I must choose one of my Big items to give to the lowest level.

Is the rule for doing this the following:

I choose which lowest level to give it to.
It must remain in play, therefore it cannot be put in their hand.

If the player I choose to give it to has a Big item and cannot legally play a 2nd Big item, do they have a choice between the one I give them and the one they currently carry?
If so, do they then have to discard one of the Big items or do they choose which player tied in levels with them to give it to?

or

Do I simply make a choice between the lowest level players that can legally carry a Big item? If none exist, simply discard it.

or

Is there another scenario I am missing?

Thank you for your time and patience. I didn't locate the answer in the FAQ and wonder if somehow I overlooked it.