Dear Rabbi Kacev:

Are there other opinions on this point? Or perhaps it changes when the candles have burned out? Or if the space is needed for something else?

We are talking here about the Din of Bassis, wherby something that forms a base for a Muktzeh item itself becomes Muktzeh. If, however, the base is a Bassis for a non-Muktzeh item then the base may not be Muktzeh.

In regard to the Shabbos candles, if one were to place (say) a Siddur on the tray with the candles, then after they have gone out it may be permissible to move the tray.

However, I believe that Rav Moshe Feinstein zt"l rules that if it is a smallish tray that is specifically for the candles then one may not rely on this permission.

If the tray may not be moved, then its type of Muktzeh is severe and it may therefore not be moved even if one needs its place.

Also, if one places the Challah on the table at the time of lighting the candles, then one may move the table if needed to make more room, once the candles have gone out. Otherwise the table becomes forbidden to move.