Actually, I wouldn't separate the various sets, or try to "buy in" ones to fit in with missing ones. Keep the whole lot together. I wouldn't pass it to a museum - recently there was a news item about some "spare" medals being put up for sale by a museum, to fund buying more interesting items!
If a relative has actually known someone during their lifetime, then I would say items would mean more to them than to someone who has not known that person.
You could easily make multiple copies of a good photographic display of the collection as it stands, and send a copy to anyone you are considering as a recipient of the actual items, without mentioning disposal of the originals.
Then sit back and see how each reacts.
The responses you get to that gift may help you to decide where best to bestow the originals - No response, then no interest; grateful thanks, and follow-up questions about things - then onto the shortlist!
Or you could divide memorabilia into lots, and allocate one lot to each, unseen, by drawing lots. I know where that was done with a collection of jewellery, it was divided into smaller collections of approximately equal value by a third party, boxed the same, another person stuck letters at random onto each, and the named recipients each chose a letter, starting with the oldest female, and had to be content with whatever was their lot ... although they did later do some "swaps".
The whole issue sounds to be stressing you so much, is it worth it? Someone is bound to be resentful, and someone delighted, in any case. Relax, and enjoy your research, leave that problem until you are no longer involved in it personally. A lot may change, over time.
